Methods for manufacturing glass articles

ABSTRACT

Methods of producing a glass article include melting a first glass composition and feeding a second glass composition into the melter. Both glass compositions include the same combination of components but at least one component has a concentration that is different in each. At least three glass articles may be drawn from the melter, including: a first glass article formed from the first glass composition; at least one intermediate glass article composed of neither the first nor the second glass composition; and a final glass article not composed of the first glass composition. The concentration of the at least one component in the intermediate glass article may be between the concentration in the first and second glass compositions. The first glass article and final glass article may have differing values for certain properties, and the intermediate glass article may have an intermediate set of values for the same properties.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a division of U.S. patent application Ser. No.16/542,585, filed Aug. 16, 2019, which claims the benefit of priority toU.S. Provisional Application Ser. No. 62/721,233 filed on Aug. 22, 2018,the content of which is relied upon and incorporated herein by referencein its entirety.

BACKGROUND Field

This disclosure relates to methods for manufacturing glass articles, andin particular, to methods for forming glass articles having targetcoefficients of thermal expansion.

Technical Background

Glass articles are used in a variety of industries, including thesemiconductor packaging industry. In the semiconductor packagingindustry, chips are placed on carrier substrates (e.g., glass plates)for processing which may include thermo-mechanical and lithographicsteps. However, processing techniques may vary among manufacturers,giving rise to different carrier requirements for differentmanufacturing techniques that, in turn, give rise to difficulties inmanufacturing a single carrier substrate design that meets all therequirements for different manufacturers.

Accordingly, a need exists for alternative methods of manufacturingglass carriers for use in semiconductor manufacturing.

SUMMARY

According to various aspects disclosed herein, a method of producing aglass article includes melting a first glass composition in a melter,the first glass composition comprising a combination of glassconstituent components. A second glass composition may then be fed intothe melter. This second glass composition includes the same combinationof glass constituent components but at least one glass constituentcomponent has a concentration that is different from the concentrationof the same component in the first glass composition. At least threeglass articles may be drawn from the melter while maintaining thecontents of the melter in a molten state, including: (1) a first glassarticle that is formed from the first glass composition; (2) at leastone intermediate glass article that is composed of neither the firstglass composition nor the second glass composition; (3) and a finalglass article that is composed of a composition that is different fromthe first glass composition. The concentration of the at least onecomponent in the at least one intermediate glass article may be betweenthe concentration of the at least one component in the first glasscomposition and the concentration of the at least one component in thesecond glass composition. The first glass article may have a first setof values for a set of properties. The final glass article may have asecond set of values for the same set of properties, the second set ofvalues being different from the first set of values. The at least oneintermediate glass article may have an intermediate set of values forthe set of properties that is between the first set of values and thesecond set of values.

Some aspects include the method of any of the foregoing aspects, whereinthe final glass article comprises the second glass composition.

Some aspects include the method of any of the foregoing aspects, whereinthe concentration of the at least one glass constituent component of thesecond glass composition is different from the concentration of the atleast one glass constituent component of the first glass composition byno more than 2 weight %.

Some aspects include the method of any of the foregoing aspects, whereinthe at least one component is selected from SiO₂, Al₂O₃, B₂O₃, Na₂O,MgO, CaO, AlF₃, and Sb₂O₃.

Some aspects include the method of any of the foregoing aspects, whereinthe at least one component comprises AlF₃.

Some aspects include the method of any of the foregoing aspects, whereinthe set of properties comprises one or more of a coefficient of thermalexpansion (“CTE”), a Young's modulus, a density, a 200 Poisetemperature, a surface quality, a refractive index, a resistivity, andan edge strength.

Some aspects include the method of any of the foregoing aspects, whereinthe CTE of the first glass article is equal to or within ±7.5×10⁻⁷/° C.different from the CTE of the final glass article.

Some aspects include the method of any of the foregoing aspects, whereinthe refractive index of the first glass article is less than or equal to±0.01 different from the refractive index of the final glass article.

Some aspects include the method of any of the foregoing aspects, whereinthe difference between the CTE of the at least one intermediate glassarticle and the CTE of the first glass article, as a percentage of theCTE of the first glass article, is greater than the difference betweenthe Young's modulus of the at least one intermediate glass article andthe Young's modulus of the first glass article, as a percentage of theYoung's modulus of the first glass article.

Some aspects include the method of any of the foregoing aspects, whereina viscosity of the composition within the melter varies by no more than25 Poise during the drawing the at least three glass articles.

Some aspects include the method of any of the foregoing aspects, whereina 200 Poise temperature of the glass mixture within the melter is lessthan or equal to 1500° C.

Some aspects include the method of any of the foregoing aspects, whereinthe at least three glass articles are in the shape of a boule.

Some aspects include the method of any of the foregoing aspects, whereinthe feeding the second glass composition is simultaneous with thedrawing the at least three glass articles.

Some aspects include the method of any of the foregoing aspects, whereinthe at least one intermediate glass article comprises at least 3 glassarticles, each having a different concentration of the at least oneglass constituent component that is between the concentration of the atleast one glass constituent component in the first glass composition andthe concentration of the at least one glass constituent component in thesecond glass composition.

Some aspects include the method of any of the foregoing aspects, whereinthe at least one intermediate glass article comprises at least 8 glassarticles, each having a different concentration of the at least oneglass constituent component that is between the concentration of the atleast one glass constituent component in the first glass composition andthe concentration of the at least one glass constituent component in thesecond glass composition.

Some aspects include the method of any of the foregoing aspects, whereinthe at least one intermediate glass article comprises at least 18 glassarticles, each having a different concentration of the at least oneglass constituent component that is between the concentration of the atleast one glass constituent component in the first glass composition andthe concentration of the at least one glass constituent component in thesecond glass composition.

Some aspects include the method of any of the foregoing aspects, whereinthe at least one intermediate glass article comprises at least 28 glassarticles, each having a different concentration of the at least oneglass constituent component that is between the concentration of the atleast one glass constituent component in the first glass composition andthe concentration of the at least one glass constituent component in thesecond glass composition.

Some aspects include the method of any of the foregoing aspects, furthercomprising feeding into the melter a third glass composition comprisingthe same combination of glass constituent components. At least one glassconstituent component has a concentration that is different from aconcentration of the same component of the first glass composition andthe second glass composition. The method further comprises drawing atleast a first additional glass article and a final additional glassarticle from the melter while maintaining the contents of the melter ina molten state. The first additional glass article has a firstadditional set of values for the set of properties and the finaladditional glass article has a final additional set of values for theset of properties.

Some aspects include the method of any of the foregoing aspects, whereinthe set of properties comprises one or more of a coefficient of thermalexpansion (“CTE”), a Young's modulus, a density, a 200 Poisetemperature, a surface quality, a refractive index, a resistivity, andan edge strength.

Some aspects include the method of any of the foregoing aspects, whereinthe CTE of the first glass article is equal to or within ±15×10⁻⁷/° C.different from the CTE of the final additional glass article.

Some aspects include the method of any of the foregoing aspects, whereinthe difference between the CTE of the first additional glass article andthe CTE of the first glass article, as a percentage of the CTE of thefirst glass article, is greater than the difference between the Young'smodulus of the first additional glass article and the Young's modulus ofthe first glass article, as a percentage of the Young's modulus of thefirst glass article.

Some aspects include the method of any of the foregoing aspects, whereina viscosity of the composition within the melter varies by no more than25 Poise during the drawing the first glass article and the drawing thefinal additional glass article.

Some aspects include the method of any of the foregoing aspects, whereina 200 Poise temperature of the glass mixture within the melter is lessthan or equal to 1500° C.

Some aspects include the method of any of the foregoing aspects, whereinthe first glass composition comprises an alkali boroaluminosilicateglass composition.

Some aspects include the method of any of the foregoing aspects, whereinthe first glass composition comprises an alkaline earthboroaluminosilicate glass composition.

Some aspects include the method of any of the foregoing aspects, whereinthe first glass composition comprises a zinc boroaluminosilicate glasscomposition.

Some aspects include the method of any of the foregoing aspects, whereinthe first glass composition comprises: greater than or equal to 60 wt %and less than or equal to 65 wt % SiO₂; greater than or equal to 1.5 wt% and less than or equal to 5.0 wt % Al₂O₃; greater than or equal to 0wt % and less than or equal to 2 wt % B₂O₃; greater than or equal to 6wt % and less than or equal to 18 wt % Na₂O; greater than or equal to 0wt % and less than or equal to 10 wt % K₂O; greater than or equal to 2wt % and less than or equal to 10 wt % MgO; greater than or equal to 0wt % and less than or equal to 2 wt % CaO; greater than or equal to 0 wt% and less than or equal to 2 wt % TiO₂; and greater than or equal to 10wt % and less than or equal to 15 wt % ZnO.

Some aspects include the method of any of the foregoing aspects, whereinthe first glass composition comprises: greater than or equal to 60 wt %and less than or equal to 65 wt % SiO₂; greater than or equal to 10 wt %and less than or equal to 15 wt % Al₂O₃; greater than or equal to 2 wt %and less than or equal to 4 wt % B₂O₃; greater than or equal to 2 wt %and less than or equal to 5 wt % Li₂O; greater than or equal to 6 wt %and less than or equal to 18 wt % Na₂O; greater than or equal to 1 wt %and less than or equal to 3 wt % MgO; and greater than or equal to 0 wt% and less than or equal to 3 wt % CaO.

Some aspects include the method of any of the foregoing aspects, whereinthe first glass composition comprises: greater than or equal to 45 wt %and less than or equal to 55 wt % SiO₂; greater than or equal to 20 wt %and less than or equal to 27 wt % Al₂O₃; greater than or equal to 8 wt %and less than or equal to 10 wt % B₂O₃; greater than or equal to 0 wt %and less than or equal to 8 wt % Na₂O; greater than or equal to 0 wt %and less than or equal to 6 wt % MgO; and greater than or equal to 7 wt% and less than or equal to 9 wt % CaO.

Some aspects include the method of any of the foregoing aspects, whereinthe first glass composition comprises: greater than or equal to 56 wt %and less than or equal to 66 wt % SiO₂; greater than or equal to 9.5 wt% and less than or equal to 12.0 wt % Al₂O₃; greater than or equal to3.0 wt % and less than or equal to 7.5 wt % Li₂O; greater than or equalto 6 wt % and less than or equal to 18 wt % Na₂O; greater than or equalto 0 wt % and less than or equal to 14 wt % K₂O; greater than or equalto 0 wt % and less than or equal to 2 wt % MgO; and greater than orequal to 0 wt % and less than or equal to 8 wt % CaO.

Some aspects include the method of any of the foregoing aspects, whereinthe first glass composition comprises: greater than or equal to 45 wt %and less than or equal to 55 wt % SiO₂; greater than or equal to 22 wt %and less than or equal to 27 wt % Al₂O₃; greater than or equal to 8 wt %and less than or equal to 10 wt % B₂O₃; greater than or equal to 0 wt %and less than or equal to 8 wt % Na₂O; greater than or equal to 0 wt %and less than or equal to 8 wt % MgO; and greater than or equal to 7 wt% and less than or equal to 12 wt % CaO.

Some aspects include the method of any of the foregoing aspects, whereinthe first glass composition comprises: greater than or equal to 35 wt %and less than or equal to 48 wt % SiO₂; greater than or equal to 17 wt %and less than or equal to 20 wt % Al₂O₃; greater than or equal to 0 wt %and less than or equal to 5 wt % Na₂O; greater than or equal to 0 wt %and less than or equal to 7 wt % K₂O; greater than or equal to 0 wt %and less than or equal to 4 wt % MgO; greater than or equal to 0 wt %and less than or equal to 8.5 wt % CaO; and greater than or equal to 25wt % and less than or equal to 32 wt % La₂O₃.

Some aspects include the method of any of the foregoing aspects, whereinthe first glass composition comprises: greater than or equal to 45 wt %and less than or equal to 55 wt % SiO₂; greater than or equal to 20 wt %and less than or equal to 27 wt % Al₂O₃; greater than or equal to 8 wt %and less than or equal to 10 wt % B₂O₃; greater than or equal to 0 wt %and less than or equal to 8 wt % Na₂O; greater than or equal to 0 wt %and less than or equal to 6 wt % MgO; greater than or equal to 7 wt %and less than or equal to 9 wt % CaO; greater than or equal to 0 wt %and less than or equal to 0.7 wt % Sb₂O₃; and greater than 0 wt % andless than or equal to 1.5 wt % AlF₃.

Some aspects include the method of any of the foregoing aspects, whereinthe first glass composition comprises: greater than or equal to 45 wt %and less than or equal to 55 wt % SiO₂; greater than or equal to 20 wt %and less than or equal to 27 wt % Al₂O₃; greater than or equal to 8 wt %and less than or equal to 10 wt % B₂O₃; greater than or equal to 0 wt %and less than or equal to 8 wt % Na₂O; greater than or equal to 0 wt %and less than or equal to 6 wt % MgO; greater than or equal to 7 wt %and less than or equal to 9 wt % CaO; greater than or equal to 0 wt %and less than or equal to 0.7 wt % Sb₂O₃; and greater than 0.5 wt % andless than or equal to 1.5 wt % AlF₃.

Some aspects include a glass article formed from a glass compositioncomprising: greater than or equal to 56 wt % and less than or equal to66 wt % SiO₂; greater than or equal to 9.5 wt % and less than or equalto 12.0 wt % Al₂O₃; greater than or equal to 3.0 wt % and less than orequal to 7.5 wt % Li₂O; greater than or equal to 6 wt % and less than orequal to 18 wt % Na₂O; greater than or equal to 0 wt % and less than orequal to 14 wt % K₂O; greater than or equal to 0 wt % and less than orequal to 2 wt % MgO; and greater than or equal to 0 wt % and less thanor equal to 8 wt % CaO.

Some aspects include a glass article formed from a glass compositioncomprising: greater than or equal to 45 wt % and less than or equal to55 wt % SiO₂; greater than or equal to 20 wt % and less than or equal to27 wt % Al₂O₃; greater than or equal to 8 wt % and less than or equal to10 wt % B₂O₃; greater than or equal to 0 wt % and less than or equal to8 wt % Na₂O; greater than or equal to 0 wt % and less than or equal to 6wt % MgO; greater than or equal to 7 wt % and less than or equal to 9 wt% CaO; greater than or equal to 0 wt % and less than or equal to 0.7 wt% Sb₂O₃; and greater than 0 wt % and less than or equal to 1.5 wt %AlF₃.

Some aspects include a method for manufacturing a glass article having atarget coefficient of thermal expansion (CTE_(T)). The method includesmelting a molten base glass composition (or a “first glass composition”)having an initial overall cation field strength, determining the targetCTE_(T) over a temperature range, and replacing an amount of a firstalkaline earth component or a first alkali component having a firstcation field strength in the molten base glass composition with anamount of a second alkaline earth component or a second alkali componenthaving a second cation field strength that is different from the firstcation field strength to produce a modified glass composition. A baseglass article formed from the molten base glass composition comprises anaverage base glass coefficient of thermal expansion CTE_(B) over thetemperature range. The modified glass composition comprising an averagecoefficient of thermal expansion CTE_(M) over the temperature range thatis within +/−1.0×10⁻⁷/° C. of the target CTE_(T) and a modified overallcation field strength that is different from the initial overall cationfield strength.

Some aspects include the method of any of the foregoing aspects, whereinthe second cation field strength is less than the first cation fieldstrength; the modified overall cation field strength is less than theinitial overall cation field strength; and CTE_(M) is greater thanCTE_(B).

Some aspects include the method of any of the foregoing aspects, whereinthe replacing comprises replacing an amount of the first alkaline earthcomponent with an amount of an alkali component.

Some aspects include the method of any of the foregoing aspects, whereinthe first alkaline earth component comprises MgO and the alkalicomponent comprises Na₂O.

Some aspects include the method of any of the foregoing aspects, whereinthe replacing comprises replacing an amount of the first alkaline earthcomponent with an amount of the second alkaline earth component.

Some aspects include the method of any of the foregoing aspects, whereinthe replacing comprises replacing an amount of the first alkalicomponent with an amount of the second alkali component.

Some aspects include the method of any of the foregoing aspects, whereinthe second cation field strength is greater than the first cation fieldstrength; the modified overall cation field strength is greater than theinitial overall cation field strength; and CTE_(M) is less than CTE_(B).

Some aspects include the method of any of the foregoing aspects, whereinthe replacing comprises replacing an amount of the first alkalicomponent with an amount of an alkaline earth component.

Some aspects include the method of any of the foregoing aspects, whereinthe first alkali component comprises Na₂O and the alkaline earthcomponent comprises MgO.

Some aspects include the method of any of the foregoing aspects, whereinthe temperature range is from 0° C. to 300° C.

Some aspects include the method of any of the foregoing aspects, whereinthe temperature range is from 20° C. to 260° C.

Some aspects include the method of any of the foregoing aspects, whereinCTE_(B) is greater than or equal to 85×10⁻⁷/° C. and less than or equalto 95×10⁻⁷/° C. over the temperature range from 20° C. to 260° C.

Some aspects include the method of any of the foregoing aspects, whereinthe target CTE_(T) is greater than or equal to 80×10⁻⁷/° C. and lessthan or equal to 100×10⁻⁷/° C. over the temperature range from 20° C. to260° C.

Some aspects include the method of any of the foregoing aspects, whereina glass article formed from the modified glass composition comprises aYoung's modulus of greater than or equal to 68 GPa.

Some aspects include the method of any of the foregoing aspects, whereinthe target CTE_(T) is greater than or equal to 75×10⁻⁷/° C. and lessthan or equal to 85×10⁻⁷/° C. over the temperature range from 20° C. to260° C.

Some aspects include the method of any of the foregoing aspects, whereina glass article formed from the modified glass composition comprises aYoung's modulus of greater than or equal to 73 GPa.

Some aspects include the method of any of the foregoing aspects, whereinthe target CTE_(T) is greater than or equal to 40×10⁻⁷/° C. and lessthan or equal to 70×10⁻⁷/° C. over the temperature range from 20° C. to260° C.

Some aspects include the method of any of the foregoing aspects, whereinthe target CTE_(T) is greater than or equal to 40×10⁻⁷/° C. and lessthan or equal to 60×10⁻⁷/° C. over the temperature range from 20° C. to260° C.

Some aspects include the method of any of the foregoing aspects, whereina glass article formed from the modified glass composition comprises aYoung's modulus of greater than or equal to 90 GPa.

Some aspects include the method of any of the foregoing aspects, whereinthe target CTE_(T) is greater than or equal to 40×10⁻⁷/° C. and lessthan or equal to 54×10⁻⁷/° C. over the temperature range from 20° C. to260° C.

Some aspects include the method of any of the foregoing aspects, whereinthe target CTE_(T) is greater than or equal to 90×10⁻⁷/° C. and lessthan or equal to 150×10⁻⁷/° C. over the temperature range from 20° C. to260° C.

Some aspects include the method of any of the foregoing aspects, whereina glass article formed from the modified glass composition comprises aYoung's modulus of greater than or equal to 65 GPa.

Some aspects include the method of any of the foregoing aspects, whereina glass article formed from the modified glass composition comprises aYoung's modulus of greater than or equal to 72 GPa.

Some aspects include the method of any of the foregoing aspects, whereinthe modified glass composition comprises a 200 P temperature of lessthan or equal to 1500° C.

Some aspects include the method of any of the foregoing aspects, whereinthe modified glass composition comprises a 200 P temperature of lessthan or equal to 1450° C.

Some aspects include the method of any of the foregoing aspects, whereinthe base glass composition comprises an alkali boroaluminosilicate glasscomposition.

Some aspects include the method of any of the foregoing aspects, whereinthe base glass composition comprises an alkaline earthboroaluminosilicate glass composition.

Some aspects include the method of any of the foregoing aspects, whereinthe base glass composition comprises a zinc boroaluminosilicate glasscomposition.

Some aspects include the method of any of the foregoing aspects, whereinthe base glass composition comprises: greater than or equal to 60 wt %and less than or equal to 65 wt % SiO₂; greater than or equal to 1.5 wt% and less than or equal to 5.0 wt % Al₂O₃; greater than or equal to 0wt % and less than or equal to 2 wt % B₂O₃; greater than or equal to 6wt % and less than or equal to 18 wt % Na₂O; greater than or equal to 0wt % and less than or equal to 10 wt % K₂O; greater than or equal to 2wt % and less than or equal to 10 wt % MgO; greater than or equal to 0wt % and less than or equal to 2 wt % CaO; greater than or equal to 0 wt% and less than or equal to 2 wt % TiO₂; and greater than or equal to 10wt % and less than or equal to 15 wt % ZnO.

Some aspects include the method of any of the foregoing aspects, whereinthe base glass composition comprises: greater than or equal to 60 wt %and less than or equal to 65 wt % SiO₂; greater than or equal to 10 wt %and less than or equal to 15 wt % Al₂O₃; greater than or equal to 2 wt %and less than or equal to 4 wt % B₂O₃; greater than or equal to 2 wt %and less than or equal to 5 wt % Li₂O; greater than or equal to 6 wt %and less than or equal to 18 wt % Na₂O; greater than or equal to 1 wt %and less than or equal to 3 wt % MgO; and greater than or equal to 0 wt% and less than or equal to 3 wt % CaO.

Some aspects include the method of any of the foregoing aspects, whereinthe base glass composition comprises: greater than or equal to 45 wt %and less than or equal to 55 wt % SiO₂; greater than or equal to 20 wt %and less than or equal to 27 wt % Al₂O₃; greater than or equal to 8 wt %and less than or equal to 10 wt % B₂O₃; greater than or equal to 0 wt %and less than or equal to 8 wt % Na₂O; greater than or equal to 0 wt %and less than or equal to 6 wt % MgO; and greater than or equal to 7 wt% and less than or equal to 9 wt % CaO.

Some aspects include the method of any of the foregoing aspects, whereinthe base glass composition comprises: greater than or equal to 45 wt %and less than or equal to 55 wt % SiO₂; greater than or equal to 22 wt %and less than or equal to 27 wt % Al₂O₃; greater than or equal to 8 wt %and less than or equal to 10 wt % B₂O₃; greater than or equal to 0 wt %and less than or equal to 8 wt % Na₂O; greater than or equal to 0 wt %and less than or equal to 8 wt % MgO; and greater than or equal to 7 wt% and less than or equal to 12 wt % CaO.

Some aspects include the method of any of the foregoing aspects, whereinthe base glass composition comprises: greater than or equal to 35 wt %and less than or equal to 48 wt % SiO₂; greater than or equal to 17 wt %and less than or equal to 20 wt % Al₂O₃; greater than or equal to 0 wt %and less than or equal to 5 wt % Na₂O; greater than or equal to 0 wt %and less than or equal to 7 wt % K₂O; greater than or equal to 0 wt %and less than or equal to 4 wt % MgO; greater than or equal to 0 wt %and less than or equal to 8.5 wt % CaO; and greater than or equal to 25wt % and less than or equal to 32 wt % La₂O₃.

Some aspects include the method of any of the foregoing aspects, furthercomprising delivering the modified glass composition to a formingvessel.

Some aspects include the method of any of the foregoing aspects, furthercomprising forming the modified glass composition into a glass boulewith the forming vessel.

Some aspects include the method of any of the foregoing aspects, whereinwhen the target CTE_(T) is greater than or equal to 80×10⁻⁷/° C. andless than or equal to 100×10⁻⁷/° C. over the temperature range from 20°C. to 260° C., determining the target CTE_(T) comprises determining thetarget CTE_(T) according to the following equation:

CTE_(T)=(−1.17[wt% SiO₂])−(1.31[wt% Al₂O₃])−(0.84[wt% B₂O₃])+(4.36[wt%Na₂O])+(0.98[wt% MgO])+(47.1[wt% TiO₂])−(0.64[wt% ZnO])+(4.45[wt%K₂O])−(37.2[wt% CaO])−117.

Some aspects include the method of any of the foregoing aspects, whereinwhen the target CTE_(T) is greater than or equal to 40×10⁻⁷/° C. andless than or equal to 70×10⁻⁷/° C. over the temperature range from 20°C. to 260° C., determining the target CTE_(T) comprises determining thetarget CTE_(T) according to the following equation:

CTE_(T)=(6.58[wt% SiO₂])+(0.67[wt% Al₂O₃])+(0.04[wt% B₂O₃])+(3.64[wt%Na₂O])+(0.59[wt% MgO])+(1.34[wt% CaO])+6.58.

Some aspects include the method of any of the foregoing aspects, whereinwhen the target CTE_(T) is greater than or equal to 90×10⁻⁷/° C. andless than or equal to 150×10⁻⁷/° C. over the temperature range from 20°C. to 260° C., determining the target CTE_(T) comprises determining thetarget CTE_(T) according to the following equation:

CTE_(T)=(137.56[wt% SiO₂])−(5.47[wt% Al₂O₃])+(1.18[wt% Li₂O])+(2.22[wt%Na₂O])+(1.32[wt% K₂O])−(5.37[wt% MgO])−(0.09[wt% CaO])+137.56.

Some aspects include a glass article formed from a glass compositionincluding greater than or equal to 56 wt % and less than or equal to 66wt % SiO₂; greater than or equal to 9.5 wt % and less than or equal to12.0 wt % Al₂O₃; greater than or equal to 3.0 wt % and less than orequal to 7.5 wt % Li₂O; greater than or equal to 6 wt % and less than orequal to 18 wt % Na₂O; greater than or equal to 0 wt % and less than orequal to 14 wt % K₂O; greater than or equal to 0 wt % and less than orequal to 2 wt % MgO; and greater than or equal to 0 wt % and less thanor equal to 8 wt % CaO.

Some aspects include the glass article of any of the foregoing aspects,comprising a coefficient of thermal expansion (C 1E) of greater than orequal to 90×10⁻⁷ and less than or equal to 150×10⁻⁷/° C. over thetemperature range from 20° C. to 260° C.

Some aspects include the glass article of any of the foregoing aspects,comprising a Young's modulus of greater than or equal to 70 GPa and lessthan or equal to 100 GPa.

Some aspects include the glass article of any of the foregoing aspects,wherein the Young's modulus is greater than or equal to 72 GPa and lessthan or equal to 85 GPa.

Some aspects include the glass article of any of the foregoing aspects,comprising a 200 Poise temperature of greater than or equal to 0° C. andless than or equal to 1500° C.

Some aspects include the glass article of any of the foregoing aspects,wherein the 200 Poise temperature is greater than or equal to 1250° C.and less than or equal to 1500° C.

Some aspects include the glass article of any of the foregoing aspects,wherein the glass composition comprises a density of greater than orequal to 2.25 g/cm³ and less than or equal to 2.75 g/cm³.

Some aspects include the glass article of any of the foregoing aspects,wherein:

13wt%<[wt% Li₂O+wt% Na₂O+wt% K₂O]<31wt%.

Various aspects disclosed herein may be combined in any permutation.

It is to be understood that both the foregoing general description andthe following detailed description are merely exemplary, and areintended to provide an overview or framework to understanding the natureand character of the claimed subject matter. The accompanying drawingsare included to provide a further understanding and are incorporated inand constitute a part of this specification. The drawings illustrate oneor more embodiment(s), and together with the description, serve toexplain principles and operation of the various embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically depicts one example glass manufacturing apparatusfor forming glass substrates in accordance with one or more embodimentsshown and described herein;

FIG. 2 is a plot of measured CTE (Y-axis; values x 10⁻⁷/° C.) as afunction of total modifier cation field strength (X-axis) in accordancewith one or more embodiments shown and described herein; and

FIG. 3 is a plot of measured CTE (Y-axis; values x 10⁻⁷/° C.) as afunction of total modifier cation field strength (X-axis) in accordancewith one or more embodiments shown and described herein;

FIG. 4 is a plot of the measured CTE (Y-axis; values x 10⁻⁷/° C.) as afunction of the predicted CTE (X-axis; values x 10⁻⁷/° C.) for exampleglass compositions in accordance with one or more embodiments shown anddescribed herein;

FIG. 5 is a plot of the measured Young's modulus (Y-axis; in GPa) as afunction of the predicted Young's modulus (X-axis; in GPa) for exampleglass compositions in accordance with one or more embodiments shown anddescribed herein;

FIG. 6 is a plot of the measured CTE (Y-axis; values x 10⁻⁷/° C.) as afunction of the predicted CTE (X-axis; values x 10⁻⁷/° C.) for differentexample glass compositions in accordance with one or more embodimentsshown and described herein;

FIG. 7 is a plot of the measured Young's modulus (Y-axis; in GPa) as afunction of the predicted Young's modulus (X-axis; in GPa) for differentexample glass compositions in accordance with one or more embodimentsshown and described herein;

FIG. 8 is a plot of the measured CTE (Y-axis; values x 10⁻⁷/° C.) as afunction of the predicted CTE (X-axis; values x 10⁻⁷/° C.) for exampleglass compositions in accordance with one or more embodiments shown anddescribed herein;

FIG. 9 is a plot of the measured Young's modulus (Y-axis; in GPa) as afunction of the predicted Young's modulus (X-axis; in GPa) for exampleglass compositions in accordance with one or more embodiments shown anddescribed herein;

FIG. 10 is a plot of the measured CTE (Y-axis; values x 10⁻⁷/° C.) as afunction of the predicted CTE (X-axis; values x 10⁻⁷/° C.) over 20° C.to 300° C. for example glass compositions in accordance with one or moreembodiments shown and described herein;

FIG. 11 is a plot of the measured CTE (Y-axis; values x 10⁻⁷/° C.) as afunction of the predicted CTE (X-axis; values x 10⁻⁷/° C.) over 20° C.to 390° C. for example glass compositions in accordance with one or moreembodiments shown and described herein;

FIG. 12 is a plot of the measured CTE (Y-axis; values x 10⁻⁷/° C.) as afunction of the predicted CTE (X-axis; values x 10⁻⁷/° C.) over 20° C.to 300° C. for example glass compositions in accordance with one or moreembodiments shown and described herein;

FIG. 13 is a plot of the measured CTE (Y-axis; values x 10⁻⁷/° C.) as afunction of the predicted CTE (X-axis; values x 10⁻⁷/° C.) over 20° C.to 390° C. for example glass compositions in accordance with one or moreembodiments shown and described herein;

FIG. 14 is a plot of the measured CTE (Y-axis; values x 10⁻⁷/° C.) as afunction of the predicted CTE (X-axis; values x 10⁻⁷/° C.) over 20° C.to 300° C. for example glass compositions in accordance with one or moreembodiments shown and described herein;

FIG. 15 is a plot of the measured CTE (Y-axis; values x 10⁻⁷/° C.) as afunction of the predicted CTE (X-axis; values x 10⁻⁷/° C.) over 20° C.to 390° C. for example glass compositions in accordance with one or moreembodiments shown and described herein;

FIG. 16 is a plot of the measured CTE of several glasses containingfluorine (Y-axis; values x 10⁻⁷/° C.) versus the CTE of those sameglasses made without fluorine (X-axis; values x 10⁻⁷/° C.) in accordancewith one or more embodiments shown and described herein;

FIG. 17 is a plot of the measured elastic modulus of several glassescontaining fluorine (Y-axis; values in GPa) versus the measured elasticmodulus of those same glasses made without fluorine (X-axis; values inGPa) in accordance with one or more embodiments shown and describedherein;

FIG. 18 is a plot of log viscosity (Y-axis; values in Poise) versustemperature (X-axis; values in ° C.) for two of the fluorine-freeproduction glasses, HS5.1 and HS5.9, compared to the same glasscompositions with 1.3 weight % fluorine and a standard production glass,QE, in accordance with one or more embodiments shown and describedherein;

FIG. 19 is a plot of the predicted CTE (Y-axis; values x 10⁻⁷/° C.)versus the measured CTE (X-axis; values x 10⁻⁷/° C.) for exemplaryfluorine-containing glass compositions in accordance with one or moreembodiments shown and described herein;

FIG. 20 is a plot of the predicted CTE (Y-axis; values x 10⁻⁷/° C.)versus the measured CTE (X-axis; values x 10⁻⁷/° C.) for exemplaryfluorine-containing glass compositions in accordance with one or moreembodiments shown and described herein;

FIG. 21 is a plot of the predicted CTE (Y-axis; values x 10⁻⁷/° C.)versus the measured CTE (X-axis; values x 10⁻⁷/° C.) for exemplaryfluorine-containing glass compositions in accordance with one or moreembodiments shown and described herein;

FIG. 22 is a plot of the predicted CTE (Y-axis; values x 10⁻⁷/° C.)versus the measured CTE (X-axis; values x 10⁻⁷/° C.) for exemplaryfluorine-containing glass compositions in accordance with one or moreembodiments shown and described herein;

FIG. 23 is a plot of the predicted Young's modulus (Y-axis; GPa) versusthe measured Young's modulus (X-axis; GPa) for exemplaryfluorine-containing glass compositions in accordance with one or moreembodiments shown and described herein;

FIG. 24 is a plot of the predicted Young's modulus (Y-axis; GPa) versusthe measured Young's modulus (X-axis; GPa) for exemplaryfluorine-containing glass compositions in accordance with one or moreembodiments shown and described herein;

FIG. 25 is a plot of the predicted Young's modulus (Y-axis; GPa) versusthe measured Young's modulus (X-axis; GPa) for exemplaryfluorine-containing glass compositions in accordance with one or moreembodiments shown and described herein;

FIG. 26 is a plot of the predicted Young's modulus (Y-axis; GPa), usingalternative models, versus the measured Young's modulus (X-axis; GPa)for exemplary fluorine-containing glass compositions in accordance withone or more embodiments shown and described herein; and

FIG. 27 is a plot of the predicted Young's modulus (Y-axis; GPa), usingalternative models, versus the measured Young's modulus (X-axis; GPa)for exemplary fluorine-containing glass compositions in accordance withone or more embodiments shown and described herein.

DETAILED DESCRIPTION

Reference will now be made in detail to various embodiments of methodsfor manufacturing glass articles having a target coefficient of thermalexpansion CTE_(T), embodiments of which are illustrated in theaccompanying drawings. Whenever possible, the same reference numeralswill be used throughout the drawings to refer to the same or like parts.The components in the drawings are not necessarily to scale, emphasisinstead being placed upon illustrating the principles of theembodiments.

The terms “glass” and “glass composition” encompass both glass materialsand glass-ceramic materials, as both classes of materials are commonlyunderstood. Likewise, the term “glass structure” encompasses structurescomprising glass.

The term “coefficient of thermal expansion” or CTE is an average CTEover a particular range of temperatures, as determined in accordancewith ASTM E228. Unless specified otherwise, the temperature range isfrom about 20° C. to about 260° C.

The elastic modulus (also referred to as Young's modulus) of thesubstrate is provided in units of gigapascals (GPa). The elastic modulusof the substrate is determined by resonant ultrasound spectroscopy onbulk samples of the substrate.

The density of the substrate is a measure of the degree of compactnessof the substrate and is provided in g/cm³. The density is determined inaccordance with ASTM C693.

The 200 Poise temperature is the temperature at which the glass meltdemonstrates a viscosity of 200 Poise and is provided in ° C. Thistemperature is determined in accordance with ASTM C965.

The surface quality of a substrate is a numerical description of theflatness or roughness of a surface and is determined using a frequencystepping interferometer, for example, a TROPEL® FLATMASTER® MSP(Multi-Surface Profiler).

The refractive index of a substrate is the ratio of the velocity oflight in a vacuum to its velocity in the substrate. As a ratio, therefractive index is unitless. The refractive index may be determined arefractometer, for example, a Bausch and Lomb Low Range PrecisionRefractometer or a Metricon Prism Coupler.

The resistivity of a substrate is a measure of the resisting power of aspecified material to the flow of an electric current and is provided inQm. The resistivity may be determined in accordance with ASTM D-257and/or ASTM D-657.

The edge strength of a substrate is a measure of the substrate's modulusof rupture and is provided in MPa. The edge strength may be determinedby performing a four-point bend of the substrate.

The viscosity of the melt is a quantity expressing the magnitude ofinternal friction, as measured by the force per unit area resisting aflow in which parallel layers unit distance apart have unit speedrelative to one another. Viscosity is provided in Poise herein and maybe determined by ASTM C965.

Numerical values, including endpoints of ranges, can be expressed hereinas approximations preceded by the term “about,” “approximately,” or thelike. In such cases, other embodiments include the particular numericalvalues. Regardless of whether a numerical value is expressed as anapproximation, two embodiments are included in this disclosure: oneexpressed as an approximation, and another not expressed as anapproximation. It will be further understood that an endpoint of eachrange is significant both in relation to another endpoint, andindependently of another endpoint.

Concentrations of the constituent components are specified in weightpercent (wt % or weight %) on an oxide basis unless otherwise specified.

The term “formed from” can mean one or more of comprises, consistsessentially of, or consists of. For example, a component that is formedfrom a particular material can comprise the particular material, consistessentially of the particular material, or consist of the particularmaterial.

Directional terms as used herein—for example up, down, right, left,front, back, top, bottom, vertical, horizontal—are made only withreference to the figures as drawn and are not intended to imply absoluteorientation unless otherwise expressly stated.

Unless otherwise expressly stated, it is in no way intended that anymethod set forth herein be construed as requiring that its steps beperformed in a specific order, nor that with any apparatus specificorientations be required. Accordingly, where a method claim does notactually recite an order to be followed by its steps, or that anyapparatus claim does not actually recite an order or orientation toindividual components, or it is not otherwise specifically stated in theclaims or description that the steps are to be limited to a specificorder, or that a specific order or orientation to components of anapparatus is not recited, it is in no way intended that an order ororientation be inferred, in any respect. This holds for any possiblenon-express basis for interpretation, including: matters of logic withrespect to arrangement of steps, operational flow, order of components,or orientation of components; plain meaning derived from grammaticalorganization or punctuation, and; the number or type of embodimentsdescribed in the specification.

As used herein, the singular forms “a,” “an” and “the” include pluralreferents unless the context clearly dictates otherwise. Thus, forexample, reference to “a” component includes aspects having two or moresuch components, unless the context clearly indicates otherwise. Also,the word “or” when used without a preceding “either” (or other similarlanguage indicating that “or” is unequivocally meant to beexclusive—e.g., only one of x or y, etc.) shall be interpreted to beinclusive (e.g., “x or y” means one or both x or y).

The term “and/or” shall also be interpreted to be inclusive (e.g., “xand/or y” means one or both x or y). In situations where “and/or” or“or” are used as a conjunction for a group of three or more items, thegroup should be interpreted to include one item alone, all the itemstogether, or any combination or number of the items. Moreover, termsused in the specification and claims such as have, having, include, andincluding should be construed to be synonymous with the terms compriseand comprising.

Unless otherwise indicated, all numbers or expressions, such as thoseexpressing dimensions, physical characteristics, and the like, used inthe specification (other than the claims) are understood to be modifiedin all instances by the term “approximately.” At the very least, and notas an attempt to limit the application of the doctrine of equivalents tothe claims, each numerical parameter recited in the specification orclaims which is modified by the term “approximately” should be construedin light of the number of recited significant digits and by applyingordinary rounding techniques.

Ranges can be expressed herein as from “about” one particular value,and/or to “about” another particular value. When such a range isexpressed, another embodiment includes from the one particular valueand/or to the other particular value. Similarly, when values areexpressed as approximations, by use of the antecedent “about,” it willbe understood that the particular value forms another embodiment. Itwill be further understood that the endpoints of each of the ranges aresignificant both in relation to the other endpoint, and independently ofthe other endpoint.

The drawings shall be interpreted as illustrating one or moreembodiments that are drawn to scale and/or one or more embodiments thatare not drawn to scale. This means the drawings can be interpreted, forexample, as showing: (a) everything drawn to scale, (b) nothing drawn toscale, or (c) one or more features drawn to scale and one or morefeatures not drawn to scale. Accordingly, the drawings can serve toprovide support to recite the sizes, proportions, and/or otherdimensions of any of the illustrated features either alone or relativeto each other. Furthermore, all such sizes, proportions, and/or otherdimensions are to be understood as being variable from 0-100% in eitherdirection and thus provide support for claims that recite such values orany and all ranges or subranges that can be formed by such values.

The terms recited in the claims should be given their ordinary andcustomary meaning as determined by reference to relevant entries inwidely used general dictionaries and/or relevant technical dictionaries,commonly understood meanings by those in the art, etc., with theunderstanding that the broadest meaning imparted by any one orcombination of these sources should be given to the claim terms (e.g.,two or more relevant dictionary entries should be combined to providethe broadest meaning of the combination of entries, etc.) subject onlyto the following exceptions: (a) if a term is used in a manner that ismore expansive than its ordinary and customary meaning, the term shouldbe given its ordinary and customary meaning plus the additionalexpansive meaning, or (b) if a term has been explicitly defined to havea different meaning by reciting the term followed by the phrase “as usedin this document shall mean” or similar language (e.g., “this termmeans,” “this term is defined as,” “for the purposes of this disclosurethis term shall mean,” etc.). References to specific examples, use of“i.e.,” use of the word “invention,” etc., are not meant to invokeexception (b) or otherwise restrict the scope of the recited claimterms. Other than situations where exception (b) applies, nothingcontained in this document should be considered a disclaimer ordisavowal of claim scope.

In the semiconductor packaging industry, different manufacturers haveoverarching carrier substrate requirements (i.e., size, shape, etc.)that are somewhat uniform. However, the property specifications (i.e.,coefficient of thermal expansion, elastic modulus, and the like) maydiffer from manufacturer to manufacturer or even from facility tofacility. For example, the thermal profile of a semiconductor packagingprocess may be unique to a specific manufacturer, which in turn, givesrise to a need for carrier substrates having thermal characteristicstailored to the specific thermal profile, such as the coefficient ofthermal expansion (CTE) or the like. In addition to particular CTErequirements, the glass carriers may also need to have certain otherproperties, such as elastic moduli, viscosity, surface quality, and edgestrength requirements to be considered suitable for use in conjunctionwith particular semiconductor packaging operations. The wide array ofproperty specifications for carrier substrates presents a uniquechallenge to manufacturers of glass substrates seeking to economicallyand efficiently mass produce carrier substrates compatible for use withdifferent packaging operations.

For example, semiconductor fabrication labs may need to perform a widearray of post-fabrication processing of the semiconductor. Thisprocessing typically includes placing the semiconductor on the carriersubstrate and then performing thermo-mechanical as well as lithographicsteps. The steps may be used to add metal connects, epoxy moldingcompounds, soldering, and the like. Historically the semiconductorpackaging industry used polymer material as the substrate carrier. Thepolymer material was sufficient for low-end chip packaging but hasproven unsatisfactory for manufacturing high-end products due to theinherent structural instability of polymers at the packaging processingtemperatures.

A recent trend in this industry is to use glass wafers (200 mm/300 mmdiameter) or panels (500 mm×500 mm) as substrates. Depending on themanufacturer and the particular steps involved in the post-fabricationprocessing, the carrier substrate may experience variable amounts ofstress and warpage throughout the post-fabrication process, andtherefore have custom CTE requirements, for example.

To simplify the process of obtaining glasses meeting these custom CTErequirements, a library of glass articles may be produced that have acomposition within a certain range (i.e., the compositions are similar)but physical properties which differ among each article in the library.This range of properties for a similar composition allows an end user toselect and test a particular glass article with a specific property todetermine the viability of using the glass article for a particularapplication without the need to specifically create an entire batch ofglass when only a few exemplary glasses may be needed to validate theprocess. Of course, a range of other properties and applications, beyondCTE in semiconductor fabrication, are contemplated and possible.

Methods described herein facilitate forming carrier substrates havingcompositions that are compatible with the processes employed by variousmanufacturers, while allowing the properties of the carrier substrates,including the CTE, to be tuned to meet the specifications of individualmanufacturers. Specifically, some embodiments described herein relate toa method of producing a glass article. In some embodiments, the methodincludes melting a first glass composition in a melter, the first glasscomposition comprising a combination of glass constituent components. Asecond glass composition may then be fed into the melter. This secondglass composition may include the same combination of glass constituentcomponents but at least one glass constituent component has aconcentration that is different from the concentration of the samecomponent in the first glass composition (sometimes referred to as the“varied component”). In some embodiments, at least three glass articlesmay be drawn from the melter while maintaining the contents of themelter in a molten state. These at least three glass articles mayinclude: (1) a first glass article that is formed from the first glasscomposition; (2) at least one intermediate glass article that iscomposed of neither the first glass composition nor the second glasscomposition and which may be drawn either simultaneously with thefeeding of the second glass composition or at some different time; (3)and a final glass article that is composed of a composition that isdifferent from the first glass composition and may be the same as ordifferent from the second glass composition. The concentration of the atleast one component in the at least one intermediate glass article maybe between the concentration of the at least one component in the firstglass composition and the concentration of the at least one component inthe second glass composition. The first glass article may have a firstset of values for a set of properties. The final glass article may havea second set of values for the same set of properties, the second set ofvalues being different from the first set of values. The at least oneintermediate glass article may have an intermediate set of values forthe set of properties that is between the first set of values and thesecond set of values.

Of course, more than a second glass composition could be added to themelter. For instance, the method may further include feeding a thirdglass composition into the melter. This third glass composition mayinclude the same combination of glass constituent components, but justas with the second glass composition described above, at least one glassconstituent component may have a concentration that differs from that ofboth the first glass composition and the second glass composition. Then,the method may further include drawing at least a first additional glassarticle and a final additional glass article from the melter whilemaintaining the contents of the melter in a molten state. The firstadditional glass article may have a first additional set of values forthe same set of properties discussed above, and the final additionalglass article may have a final additional set of values for the same setof properties.

In some embodiments, the concentration of the varied component in thefirst glass composition may be different from that in the second glasscomposition by no more than 2 weight %. For instance, the concentrationof the varied component in the first glass composition may be differentfrom that in the second glass composition by no more than 1.9 weight %,1.8 weight %, 1.7 weight %, 1.6 weight %, 1.5 weight %, 1.4 weight %,1.3 weight %, 1.2 weight %, 1.1 weight %, 1 weight %, 0.9 weight %, 0.8weight %, 0.7 weight %, 0.6 weight %, 0.5 weight %, 0.4 weight %, 0.3weight %, 0.2 weight %, 0.1 weight %, or any fractional part thereof.Further, all of the components of the first glass composition may havedifferent concentrations in the second glass composition or all thecomponents except one may retain the concentration present in the firstglass composition. Thus, the concentration of one component, twocomponents, three components, and so on, up to and including theconcentration of all the components of the first glass composition, maybe different in the second glass composition.

The at least one component, the concentration of which may differbetween the first and second glass compositions, i.e. the variedcomponent, may be any of the constituent components. Exemplary variedcomponents include, but are not limited to, SiO₂, Al₂O₃, B₂O₃, Na₂O,MgO, CaO, AlF₃, and Sb₂O₃. In one embodiment, the varied component isAlF₃. Although AlF₃ may not be present (i.e. 0 weight %) in someembodiments, in other embodiments, AlF₃ may be present from greater than0 weight % to less than or equal to about 1.5 weight %. In furtherembodiments, AlF₃ may be present from greater than or equal to 0.5weight % to less than or equal to about 1.5 weight %.

As noted above, the first glass article may have a first set of valuesfor a set of properties, the final glass article may have a second setof values, and the at least one intermediate glass article may have anintermediate set of values. Such properties may include, but are notlimited to, CTE, Young's modulus, density, 200 Poise temperature,surface quality, refractive index, resistivity, and edge strength. Insome embodiments, the CTE of the first glass article may be equal to orwithin ±7.5×10⁻⁷/° C. different from the CTE of the final glass article.In some embodiments, where a third glass composition is added to themelter, the CTE of the first glass article may be equal to or within±15×10⁻⁷/° C. different from the CTE of the final additional glassarticle. In the same or different embodiments, the refractive index ofthe first glass article may be less than or equal to ±0.01 differentfrom the refractive index of the final glass article.

Certain properties may remain substantially unchanged throughout themethod, including the draws of all glass articles. For instance, in someembodiments, the viscosity of the composition within the melter may varyby no more than 25 Poise during the drawing the at least three glassarticles. In the same or different embodiments, the 200 Poisetemperature of the glass mixture within the melter may be less than orequal to 1500° C. Similar effects may be observed when more than asecond glass composition, e.g., a third glass composition, is added tothe melter.

In some embodiments, the value of only one property of a set ofproperties differs between the first, final, and intermediate glassarticles. In other embodiments, all such values differ. In furtherembodiments, the values of any number of properties of a set ofproperties, from a single property to all properties, may differ betweenthe first, final, and intermediate glass articles.

In some embodiments, the values of two or more properties may not differto the same extent between the first, final, and intermediate glassarticles. For instance, the value of one property may differ to a muchlarger degree than the value of another property. In some embodiments,for example, the difference between the CTE of the at least oneintermediate glass article and the CTE of the first glass article, as apercentage of the CTE of the first glass article, may be greater thanthe difference between the Young's modulus of the at least oneintermediate glass article and the Young's modulus of the first glassarticle, as a percentage of the Young's modulus of the first glassarticle. Similar effects may be observed when more than a second glasscomposition, e.g., a third glass composition, is added to the melter.

The shape of the glass articles produced is not particularly limited. Anexemplary shape includes, but is not limited to, a glass boule. Anynumber of glass articles with different and unique glass compositionsmay be drawn from the melter. For example, hundreds, or even thousands,of glass articles may be drawn. A smaller number may also be drawn. Forexample, at least 5 glass articles may be drawn, i.e., the first glassarticle, the final glass article, and 3 intermediate glass articles. Inthe same or different embodiments, at least 10 glass articles may bedrawn, i.e., at least 8 intermediate glass articles. Similarly, in thesame or different embodiments, at least 20 glass articles may be drawn,i.e., at least 18 intermediate glass articles. Similarly, in the same ordifferent embodiments, at least 30 glass articles may be drawn, i.e., atleast 28 intermediate glass articles. Similar numbers of glass articlesmay be drawn when more than a second glass composition, e.g., a thirdglass composition, is added to the melter, but of course, even moreglass articles could be drawn under such conditions. Due to the changein the concentration of the at least one component between the first andsecond glass compositions, the glass composition drawn changes slowlyover time from that of the first glass composition to that of the secondglass composition. Each intermediate article may be drawn at a differenttime. So, each intermediate article has a different concentration of theat least one glass constituent component that is between theconcentration of the at least one glass constituent component in thefirst glass composition and the concentration of the at least one glassconstituent component in the second glass composition. If twointermediate articles are drawn at about the same time, the differencein composition may be slight. As more time passes, the difference incomposition may become more pronounced.

Referring now to FIG. 1 , an example glass manufacturing apparatus 100for forming a library of glass articles from molten glass isschematically depicted according to one or more embodiments describedherein. The glass manufacturing apparatus 100 includes a melting vessel1, a fining vessel 3, a mixing vessel 4, a delivery vessel 8, and aforming vessel 10. Glass batch materials are introduced into the meltingvessel 1 as indicated by arrow 2. The batch materials, including batchoxides, are melted to form molten glass 6. The melting vessel 1 mayinclude heating elements (not shown) for melting the batch materials.The fining vessel 3 has a high temperature processing area that receivesthe molten glass 6 from the melting vessel 1 and in which bubbles areremoved from the molten glass 6. The fining vessel 3 is fluidly coupledto the mixing vessel 4 by a connecting tube 5. That is, molten glassflowing from the fining vessel 3 to the mixing vessel 4 flows throughthe connecting tube 5. The mixing vessel 4 is, in turn, fluidly coupledto the delivery vessel 8 by a connecting tube 7 such that molten glassflowing from the mixing vessel 4 to the delivery vessel 8 flows throughthe connecting tube 7.

The delivery vessel 8 supplies the molten glass 6 through a downcomer 9into the forming vessel 10. The delivery vessel 8 may include heatingelements (not shown) for heating and/or maintaining the glass in amolten state. In some embodiments, the delivery vessel 8 may cool andcondition the molten glass in order to increase the viscosity of theglass prior to providing the glass to the forming vessel 10. The formingvessel 10 may be, for example, a fusion draw device, a slot draw deviceor a mold. The form of the resulting glass article will vary dependingon the particular forming vessel 10 employed. However, in someembodiments, the glass article resulting from the forming vessel 10 maybe in the form of a glass boule, which may then be formed into a glassplate. As the composition in the melter is varied, the resulting glassarticles will exhibit different properties due to slightly differentcomposition of each.

One convenient application for the methods described herein is tomanufacture a library of glass articles having a range of target CTE_(T)that can be achieved by making changes to a base glass composition. Insome embodiments, the method includes replacing an amount of a firstalkaline earth component or a first alkali component having a firstcation field strength in the molten base glass composition with anamount of a second alkaline earth component or a second alkali componenthaving a second cation field strength that is different from the firstcation field strength. Without being bound by theory, it is believedthat the CTE of an oxide glass depends on the strength of the bondsbetween the cations and the oxygen network. Accordingly, adjusting theoverall cation field strength of the glass can be an effective driver tochange the CTE of a resultant glass article, as will be described ingreater detail below.

In some embodiments described herein, the CTE of the glass article maybe selectively modified, or “tuned,” by adjusting the amounts of variousbatch oxides added to the melting vessel 1, replacing one or more batchoxides with a different batch oxide. As used herein, the term “replaced”means that a batch oxide may be reduced in amount or even eliminatedfrom the glass composition and a different batch oxide may be added tothe glass composition or increased in amount. In embodiments in whichthe glass manufacturing process is a continuous method, replacement ofone batch oxide with another batch oxide may include adding amounts ofother batch oxides to the melting vessel 1 and not adding additionalamounts of the batch oxide being replaced such that, over time, thebatch oxide being replaced is reduced or eliminated from the moltenglass composition in the melting vessel 1. Accordingly, the one or morebatch oxides to be replaced may be replaced in the glass batch oxidesintroduced to the melting vessel 1 and ultimately may become the moltenglass 6.

In some embodiments, an amount of one or more batch oxides (e.g., afirst alkaline earth component or a first alkali component having afirst cation field strength) in the molten base glass composition may bereplaced with an amount of a different batch oxide (e.g., a secondalkaline earth component or a second alkali component having a secondcation field strength that is different from the first cation fieldstrength) to achieve a target coefficient of thermal expansion CTE_(T)by modifying the overall cation field strength for the glasscomposition. That is, it has been determined that the coefficient ofthermal expansion of the glass composition is related to the overallcation field strength of the glass composition. For example, if thetarget CTE_(T) is greater than the coefficient of thermal expansion ofthe base glass CTE_(B), the overall cation field strength for the glasscomposition should be decreased to achieve the target CTE_(T), whereasif the target CTE_(T) is less than the base glass CTE_(B), the overallcation field strength for the glass composition should be increased toachieve the target CTE_(T). As used herein, the terms “base glass” and“base glass composition” refer to an initial base glass compositionprior to modifications. The base glass composition may also be referredto as a “first glass composition.” The resulting, or modified base glasscomposition, is referred to herein as the “modified glass” or “modifiedglass composition.” The modified glass composition may also be referredto as a “second glass composition,” as well as a “third glasscomposition.”

The cation field strength of a cation may be represented as Z/r², whereZ is the charge (unitless) of the cation and r is the radius (inAngstrom) of the cation. The overall cation field strength of a glasscomposition is calculated as follows: the molar fraction of only certainoxides is calculated first. For purposes of the present application,only the following oxides are considered in the overall cation fieldstrength calculation: SiO₂, Na₂O, CaO, MgO, Al₂O₃, K₂O, Li₂O, and ZnO.The number of cations/molecule is then multiplied by the mole fractionand the field strength for each cation to obtain the contribution to theoverall cation field strength from each oxide. The overall cation fieldstrength is the sum of each oxide contribution. Table 1 provides cationfield strength values for various cations that may be included in thebatch oxides.

TABLE 1 Cation Field Strength in Silicate Glasses* Cation Field strengthAlkali Li⁺¹ 0.26 Na⁺¹ 0.18 K⁺¹ 0.12 Cs⁺¹ 0.11 Rb⁺¹ 0.10 Alkaline EarthMg⁺² 0.46 Ca⁺² 0.36 Sr⁺² 0.29 Ba⁺² 0.26 *G. E. Brown, F. Farges, and G.Calas, Rev. Mineral., 32, 317-410, 1995.

One method of hardening these glasses is ion exchange hardening. FIGS. 2and 3 are exemplary plots of measured CTE (Y-axis; values x 10⁻⁷/° C.)as a function of total modifier cation field strength (X-axis). As maybe seen from the R² value of FIGS. 2 and 3 , the CTE is highlycorrelated with the total modifier cation field strength. In thisexample, when MgO is ion exchanged for Na₂O and CaO, the CTE ranges fromabout 45×10⁻⁷/° C. to about 65×10⁻⁷/° C., with increasing field strengthassociated with decreasing CTE. Similarly, when MgO and CaO are ionexchanged for K₂O, the CTE ranges from about 80×10⁻⁷/° C. to about100×10⁻⁷/° C., with increasing field strength associated with decreasingCTE.

In order to achieve the desired overall cation field strength (and thusthe target CTE_(T)) for the glass composition, an amount of a firstalkaline earth component in the batch oxides can be replaced with anamount of a second alkaline earth component, an amount of a first alkalicomponent in the batch oxides can be replaced with an amount of a secondalkali component, an amount of an alkaline earth component in the batchoxides can be replaced with an amount of an alkali component, or anamount of an alkali component in the batch oxides can be replaced withan amount of an alkaline earth component. In some embodiments an amountof any component may be replaced by an amount of any other component.

For example, if the target CTE_(T) is greater than the base glassCTE_(B), in some embodiments, an amount of a first alkaline earthcomponent in the base glass composition may be replaced with an amountof an alkali component or with an amount of a second alkaline earthcomponent having a cation field strength that is less than the cationfield strength of the first alkaline earth component. In someembodiments, an amount of a first alkali component in the base glasscomposition may be replaced with an amount of a second alkali componenthaving a cation field strength that is less than the cation fieldstrength of the first alkali component. For example, in someembodiments, an amount of MgO is replaced with an amount of Na₂O.

As another example, if the target CTE_(T) is less than the base glassCTE_(B), in some embodiments, an amount of a first alkali component inthe base glass composition may be replaced with an amount of an alkalineearth component or with an amount of a second alkali component having acation field strength that is greater than the cation field strength ofthe first alkali component. In some embodiments, an amount of a firstalkaline earth component in the base glass composition may be replacedwith an amount of a second alkaline earth component having a cationfield strength that is greater than the cation field strength of thefirst alkaline earth component. For example, in some embodiments, anamount of Na₂O is replaced with an amount of MgO.

In embodiments, an amount of one or more batch components to be replacedmay be determined based on the target CTE_(T) using mathematicalmodeling including, without limitation, linear modeling. The particularmodel to be used depends on the embodiment, and may vary depending onfactors including the base glass composition and the temperature rangeat which the CTE is measured. Accordingly, in embodiments, the methodincludes melting a base glass composition, forming a glass article fromthe base glass composition, modifying the base glass composition to formtwo or more modified base glass compositions, forming glass articlesfrom each of the modified base glass compositions, measuring the CTE ofeach of the glass articles made from the base glass composition and themodified base glass compositions, and developing a linear regressionbased on the measured CTE of the glass articles and the glasscomposition of the glass articles. The number of glass compositions usedin the linear regression analysis may vary depending on the particularembodiment. However, it should be understood that the number of glasscompositions employed should be sufficient to result in a meaningfullinear regression analysis.

The base glass composition may be any one of a number of suitable glasscompositions. For example, the base glass composition may be an alkaliboroaluminosilicate glass composition, an alkaline earthboroaluminosilicate glass composition, a zinc boroaluminosilicate glasscomposition, or the like. The glass composition may be selected based onits CTE at a particular temperature or over a range of temperatures(e.g., 0° C. to 400° C., 0° C. to 300° C., 0° C. to 260° C., 20° C. to300° C., or 20° C. to 260° C.), its density, its Young's modulus, its200 Poise temperature, or other properties that may be desired forprocessing or use of the glass article. The 200 Poise temperature is theminimum temperature at which the glass has a viscosity of 200 Poise,which is indicative of a minimum temperature of a well-melted glass.

The glass compositions may generally include a combination of SiO₂,Al₂O₃, at least one alkaline earth oxide and/or alkali oxides, such asNa₂O and K₂O. In some embodiments, the glass compositions may furtherinclude minor amounts of one or more additional oxides, such as, by wayof example and not limitation, SnO₂, Sb₂O₃, ZrO₂, ZnO, or the like.These components may be added as fining agents and/or to further modifythe CTE of the glass composition.

In embodiments, the glass composition generally includes SiO₂ in anamount greater than or equal to 35 wt % and less than or equal to 75 wt%. When the content of SiO₂ is too small, it becomes difficult to obtaina crystallized glass having suitable impact resistance. On the otherhand, when the content of SiO₂ is too large, melting ability of theglass decreases and the viscosity increases, so forming of the glassbecomes difficult. In some embodiments, SiO₂ is present in the glasscomposition in an amount greater than or equal to 60 wt % and less thanor equal to 65 wt %, greater than or equal to 56 wt % and less than orequal to 66 wt %, greater than or equal to 45 wt % and less than orequal to 55 wt %, greater than or equal to 35 wt % and less than orequal to 48 wt %, greater than or equal to 35 wt %, or even greater thanor equal to 45 wt %.

The glass compositions may also include Al₂O₃. Al₂O₃, in conjunctionwith alkali oxides present in the glass composition, such as Na₂O or thelike, improves the susceptibility of the glass to ion exchangestrengthening. Moreover, increased amounts of Al₂O₃ may also increasethe softening point of the glass, thereby reducing the formability ofthe glass. The glass compositions described herein may include Al₂O₃ inan amount greater than or equal to 1.5 wt % and less than or equal to 27wt %, greater than or equal to 1.5 wt % and less than or equal to 5 wt%, greater than or equal to 8 wt % and less than or equal to 15 wt %,greater than or equal to 10 wt % and less than or equal to 15 wt %,greater than or equal to 9.5 wt % and less than or equal to 12 wt %,greater than or equal to 17 wt % and less than or equal to 20 wt %, orgreater than or equal to 22 wt % and less than or equal to 27 wt %.

In some embodiments described herein, the boron concentration in theglass compositions from which the glass articles are formed is a flux,which may be added to glass compositions to make theviscosity-temperature curve less steep as well as lowering the entirecurve, thereby improving the formability of the glass and softening theglass. In embodiments, the glass compositions include greater than orequal to 0 wt % B₂O₃ and less than or equal to 2 wt % B₂O₃, greater thanor equal to 2 wt % and less than or equal to 4 wt % B₂O₃, greater thanor equal to 8 wt % and less than or equal to 10 wt % B₂O₃, or greaterthan or equal to 10 wt % and less than or equal to 15 wt % B₂O₃. In someembodiments, the glass compositions may be free from boron and compoundscontaining boron.

Embodiments of the glass compositions may further include one or morealkali oxides (e.g., Na₂O, K₂O, Li₂O, or the like). The alkali oxidesfacilitate the melting of the glass composition, lower the 200 Poisetemperature, and lower the softening point of the glass, therebyoffsetting the increase in the softening point due to higherconcentrations of SiO₂ and/or Al₂O₃ in the glass composition. The alkalioxides also assist in improving the chemical durability of the glasscomposition and tuning the CTE to a desired value. The alkali oxides aregenerally present in the glass composition in an amount greater than orequal to 6 wt % and less than or equal to 40 wt %. In some embodiments,the amount of alkali oxides may be greater than or equal to 6 wt % andless than or equal to 28 wt %, greater than or equal to 8 wt % and lessthan or equal to 23 wt %, greater than or equal to 9 wt % and less thanor equal to 17 wt %, or greater than or equal to 1 wt % and less than orequal to 8 wt %. In all of the glass compositions described herein, thealkali oxides include at least Na₂O and K₂O. Some embodiments the alkalioxides further include Li₂O.

In order to achieve the desired CTE, embodiments of the glasscompositions include Na₂O in an amount greater than or equal to 1 wt %and less than or equal to 18 wt %, greater than or equal to 6 wt % andless than or equal to 18 wt %, greater than or equal to 0 wt % and lessthan or equal to 8 wt %, greater than or equal to 0 wt % and less thanor equal to 5 wt %, or greater than or equal to 1 wt % and less than orequal to 8 wt %.

The concentration of K₂O in the glass also influences the CTE of theglass composition. Accordingly, in some embodiments, the amount of K₂Ois greater than or equal to 0 wt % and less than or equal to 14 wt %,greater than or equal to 0 wt % and less than or equal to 10 wt %, orgreater than or equal to 0 wt % and less than or equal to 7 wt %,greater than 0 wt % and less than or equal to 14 wt %, greater than 0 wt% and less than or equal to 10 wt %, or greater than 0 wt % and lessthan or equal to 7 wt %.

In embodiments of the glass composition that include Li₂O, the Li₂O maybe present in an amount greater than or equal to 2 wt % and less than orequal to 7.5 wt %, greater than or equal to 2 wt % and less than orequal to 5 wt %, or greater than or equal to 3 wt % and less than orequal to 7.5 wt %. However, in some embodiments, the glass compositionmay be substantially free of lithium and compounds containing lithium.

As provided hereinabove, embodiments of the glass compositions mayfurther include one or more alkaline earth oxides. The alkaline earthoxide may include, for example, MgO, CaO, SrO, or combinations thereof.Alkaline earth oxides improve the meltability of the glass batch oxidesand increase the chemical durability of the glass composition, inaddition to influencing the CTE. In the glass compositions describedherein, the glass compositions generally include at least one alkalineearth oxide in an amount greater than or equal to 1 wt % and less thanor equal to 22 wt %, greater than or equal to 2 wt % and less than orequal to 12 wt %, greater than or equal to 1 wt % and less than or equalto 6 wt %, greater than or equal to 9 wt % and less than or equal to 22wt %, greater than or equal to 12.5 wt % and less than or equal to 21 wt%, greater than or equal to 7 wt % and less than or equal to 20 wt %,greater than 0 wt % and less than or equal to 12.5 wt %, or greater than0 wt % and less than or equal to 10 wt %.

MgO may be present in an amount from greater than or equal to 0 wt % toless than or equal to 12 wt %, greater than or equal to 1 wt % and lessthan or equal to 10 wt %, greater than or equal to 2 wt % and less thanor equal to 10 wt %, greater than or equal to 1 wt % and less than orequal to 3 wt %, greater than or equal to 9 wt % and less than or equalto 12 wt %, greater than 0 wt % and less than or equal to 8 wt %, oreven greater than 0 wt % and less than or equal to 4 wt %. However, itis contemplated that in some embodiments, MgO may not be included in theglass composition.

As another example, CaO may be present in the glass composition in anamount from greater than or equal to 0 wt % to less than or equal to 12wt %. In embodiments, CaO may be present in an amount of from greaterthan 0 wt % to less than or equal to 8.5 wt %, greater than 0 wt % toless than or equal to 8 wt %, greater than 0 wt % to less than or equalto 3 wt %, greater than 0 wt % to less than or equal to 2 wt %, greaterthan or equal to 3 wt % to less than or equal to 6 wt %, greater than orequal to 7 wt % to less than or equal to 12 wt %, or greater than orequal to 8 wt % to less than or equal to 12 wt %. In some embodiments,CaO may be not be present in the glass composition.

In some embodiments, SrO may be included in the glass composition in anamount greater than 0.5 wt % and less than or equal to 3 wt %. In someembodiments, SrO may not be present in the glass composition.

In addition to the SiO₂, Al₂O₃, alkali oxides and alkaline earth oxides,a first embodiment of exemplary base glass compositions may optionallyinclude one or more fining agents, such as, by way of example and notlimitation, SnO₂, Sb₂O₃, As₂O₃, F⁻, and/or Cl⁻ (from NaCl or the like).When a fining agent is present in the glass composition, the finingagent may be present in amount less than or equal to 1 wt % or even lessthan or equal to 0.5 wt %. When the content of the fining agent is toolarge, the fining agent may enter the glass structure and affect variousglass properties. However, when the content of the fining agent is toolow, the glass may be difficult to form. For example, in someembodiments, SnO₂ is included as a fining agent in an amount greaterthan or equal to 0.25 wt % to less than or equal to 0.50 wt %.

Other metal oxides may additionally be included in the glasscompositions of some embodiments. For example, the glass composition mayfurther include ZnO or ZrO₂, each of which improves the resistance ofthe glass composition to chemical attack. In such embodiments, theadditional metal oxide may be present in an amount greater than or equalto 10 wt % and less than or equal to 15 wt %. For example, the glasscomposition may include ZrO₂ in an amount less than or equal to 15 wt %.If the content of ZrO₂ is too high, it may not dissolve in the glasscomposition, may result in defects in the glass composition, and maydrive the Young's modulus up. In embodiments, ZnO may be included in anamount of less than or equal to 15 wt %, or less than or equal to 12 wt%. In some embodiments, ZnO may be included as a substitute for one ormore of the alkaline earth oxides, such as a partial substitute for MgOor in addition to or in place of at least one of CaO or SrO.Accordingly, the content of ZnO in the glass composition can have thesame effects as described above with respect to alkaline earth oxides ifit is too high or too low.

In some embodiments, the base glass composition comprises greater thanor equal to 60 wt % and less than or equal to 65 wt % SiO₂, greater thanor equal to 1.5 wt % and less than or equal to 5.0 wt % Al₂O₃, greaterthan or equal to 0 wt % and less than or equal to 2 wt % B₂O₃, greaterthan or equal to 6 wt % and less than or equal to 18 wt % Na₂O, greaterthan or equal to 0 wt % and less than or equal to 10 wt % K₂O, greaterthan or equal to 2 wt % and less than or equal to 10 wt % MgO, greaterthan or equal to 0 wt % and less than or equal to 2 wt % CaO, greaterthan or equal to 0 wt % and less than or equal to 2 wt % TiO₂, andgreater than or equal to 10 wt % and less than or equal to 15 wt % ZnO.

In some embodiments, the base glass composition comprises greater thanor equal to 60 wt % and less than or equal to 65 wt % SiO₂, greater thanor equal to 10 wt % and less than or equal to 15 wt % Al₂O₃, greaterthan or equal to 2 wt % and less than or equal to 4 wt % B₂O₃, greaterthan or equal to 2 wt % and less than or equal to 5 wt % Li₂O, greaterthan or equal to 6 wt % and less than or equal to 18 wt % Na₂O, greaterthan or equal to 1 wt % and less than or equal to 3 wt % MgO, andgreater than or equal to 0 wt % and less than or equal to 3 wt % CaO.

In some embodiments, the base glass composition comprises greater thanor equal to 45 wt % and less than or equal to 55 wt % SiO₂; greater thanor equal to 20 wt % and less than or equal to 27 wt % Al₂O₃; greaterthan or equal to 8 wt % and less than or equal to 10 wt % B₂O₃; greaterthan or equal to 0 wt % and less than or equal to 8 wt % Na₂O; greaterthan or equal to 0 wt % and less than or equal to 6 wt % MgO; andgreater than or equal to 7 wt % and less than or equal to 9 wt % CaO.

In some embodiments, the base glass composition comprises greater thanor equal to 56 wt % and less than or equal to 66 wt % SiO₂, greater thanor equal to 9.5 wt % and less than or equal to 12.0 wt % Al₂O₃, greaterthan or equal to 3.0 wt % and less than or equal to 7.5 wt % Li₂O,greater than or equal to 6 wt % and less than or equal to 18 wt % Na₂O,greater than or equal to 0 wt % and less than or equal to 14 wt % K₂O,greater than or equal to 0 wt % and less than or equal to 2 wt % MgO,and greater than or equal to 0 wt % and less than or equal to 8 wt %CaO.

In some embodiments, the base glass composition comprises greater thanor equal to 45 wt % and less than or equal to 55 wt % SiO₂, greater thanor equal to 22 wt % and less than or equal to 27 wt % Al₂O₃, greaterthan or equal to 8 wt % and less than or equal to 10 wt % B₂O₃, greaterthan or equal to 0 wt % and less than or equal to 8 wt % Na₂O, greaterthan or equal to 0 wt % and less than or equal to 8 wt % MgO, andgreater than or equal to 7 wt % and less than or equal to 12 wt % CaO.

In some embodiments, the base glass composition comprises greater thanor equal to 35 wt % and less than or equal to 48 wt % SiO₂, greater thanor equal to 17 wt % and less than or equal to 20 wt % Al₂O₃, greaterthan or equal to 0 wt % and less than or equal to 5 wt % Na₂O, greaterthan or equal to 0 wt % and less than or equal to 7 wt % K₂O, greaterthan or equal to 0 wt % and less than or equal to 4 wt % MgO, greaterthan or equal to 0 wt % and less than or equal to 8.5 wt % CaO, andgreater than or equal to 25 wt % and less than or equal to 32 wt %La₂O₃.

In some embodiments, the base glass composition comprises greater thanor equal to 45 wt % and less than or equal to 55 wt % SiO₂; greater thanor equal to 20 wt % and less than or equal to 27 wt % Al₂O₃; greaterthan or equal to 8 wt % and less than or equal to 10 wt % B₂O₃; greaterthan or equal to 0 wt % and less than or equal to 8 wt % Na₂O; greaterthan or equal to 0 wt % and less than or equal to 6 wt % MgO; greaterthan or equal to 7 wt % and less than or equal to 9 wt % CaO; greaterthan or equal to 0 wt % and less than or equal to 0.7 wt % Sb₂O₃; andgreater than 0 wt % and less than or equal to 1.5 wt % AlF₃.

In some embodiments, the base glass composition comprises greater thanor equal to 45 wt % and less than or equal to 55 wt % SiO₂; greater thanor equal to 20 wt % and less than or equal to 27 wt % Al₂O₃; greaterthan or equal to 8 wt % and less than or equal to 10 wt % B₂O₃; greaterthan or equal to 0 wt % and less than or equal to 8 wt % Na₂O; greaterthan or equal to 0 wt % and less than or equal to 6 wt % MgO; greaterthan or equal to 7 wt % and less than or equal to 9 wt % CaO; greaterthan or equal to 0 wt % and less than or equal to 0.7 wt % Sb₂O₃; andgreater than 0.5 wt % and less than or equal to 1.5 wt % AlF₃.

In some embodiments, the base glass composition comprises greater thanor equal to 45 wt % and less than or equal to 55 wt % SiO₂; greater thanor equal to 20 wt % and less than or equal to 27 wt % Al₂O₃; greaterthan or equal to 8 wt % and less than or equal to 10 wt % B₂O₃; greaterthan or equal to 0 wt % and less than or equal to 8 wt % Na₂O; greaterthan or equal to 0 wt % and less than or equal to 6 wt % MgO; greaterthan or equal to 7 wt % and less than or equal to 9 wt % CaO; greaterthan or equal to 0 wt % and less than or equal to 0.7 wt % Sb₂O₃; andgreater than 0 wt % and less than or equal to 1.5 wt % AlF₃.

As described above, following selection of a base glass composition, alinear regression analysis may be performed to develop a linearregression equation relating the coefficient of thermal expansion to theconcentrations of the constituent components of the glass composition.In embodiments, the linear regression fit to the plurality of glasscompositions may be used to determine a particular amount of one or moreconstituents needed to achieve the target CTE_(T). For example, thelinear regression fit can provide a coefficient for each of theconstituents in the glass batch mixture. In some embodiments, the targetCTE_(T) over the temperature range from 20° C. to 260° C. may bedetermined according to the following equation:

CTE_(T)=(−1.17[wt% SiO₂])−(1.31[wt% Al₂O₃])−(0.84[wt% B₂O₃])+(4.36[wt%Na₂O])+(0.98[wt% MgO])+(47.1[wt% TiO₂])−(0.64[wt% ZnO])+(4.45[wt%K₂O])−(37.2[wt% CaO])−117.

In some embodiments, the target CTE_(T) over the temperature range from20° C. to 260° C. may be determined according to the following equation:

CTE_(T)=(6.58[wt% SiO₂])+(0.67[wt% Al₂O₃])+(0.04[wt% B₂O₃])+(3.64[wt%Na₂O])+(0.59[wt% MgO])+(1.34[wt% CaO])+6.58.

In some embodiments, the target CTE_(T) over the temperature range from20° C. to 260° C. may be determined according to the following equation:

CTE_(T)=(137.56[wt% SiO₂])−(5.47[wt% Al₂O₃])+(1.18[wt% Li₂O])+(2.22[wt%Na₂O])+(1.32[wt% K₂O])−(5.37[wt% MgO])−(0.09[wt% CaO])+137.56.

In some embodiments, the target CTE_(T) over the temperature range from20° C. to 260° C. may be determined according to the following equation:

CTE_(T) = (156.52[wt%SiO₂]) − (3.41[wt%Al₂O₃]) − (6.38[wt%B₂O₃]) + (4.7[wt%Na₂O]) + (3.56[wt% MgO]) − (0.62[wt%CaO]) − ? + ??indicates text missing or illegible when filed

In some embodiments, the target CTE_(T) over the temperature range from20° C. to 260° C. may be determined according to the following equation:

CTE_(T)=(142.70[wt% SiO₂])−(2.62[wt% Al₂O₃])−(8.08[wt% B₂O₃])+(0.45[wt%CaO])−(8.99[wt% F])+(4.35[wt% MgO])+(4.31[wt% Na₂O])+142.70.

In some embodiments, the target CTE_(T) over the temperature range from20° C. to 260° C. may be determined according to the following equation:

CTE_(T) = (115.77[wt%SiO₂]) + (0.07[wt%Al₂O₃]) − (4.24[wt%B₂O₃]) + (3.72[wt% Na₂O]) − (3.00[wt% MgO]) − (1.38[wt%CaO]) − ? + ?.?indicates text missing or illegible when filed

In some embodiments, the target CTE_(T) over the temperature range from20° C. to 260° C. may be determined according to the following equation:

CTE_(T)=(119.24[wt% SiO₂])+(0.20[wt% Al₂O₃])−(3.20[wt% B₂O₃])−(1.95[wt%CaO])−(0.86[wt% F])−(5.48[wt% MgO])+(3.20[wt% Na₂O])+119.24.

Other equations based on linear regression modeling are contemplated.The specific linear regression and coefficients can vary based on thebase glass composition, the target CTE_(T), and the range oftemperatures over which the CTE is measured. Accordingly, the targetCTE_(T) may be inserted into the equation and the equation may be solvedto determine the concentration of the batch oxides to form a modifiedglass composition with a modified coefficient of thermal expansionCTE_(M) closely approximating the target CTE_(T).

A linear regression analysis may also be performed to develop a linearregression equation relating the Young's modulus to the concentrationsof the constituent components of the glass composition. In embodiments,the linear regression fit to the plurality of glass compositions may beused to determine a particular amount of one or more constituents neededto achieve the target Young's modulus (ET). For example, the linearregression fit can provide a coefficient for each of the constituents inthe glass batch mixture. In some embodiments, the target ET may bedetermined according to the following equation:

E_(T) = (4.77[wt%SiO₂]) − (4.31[wt%Al₂O₃]) − (3.33[wt%B₂O₃]) + (1.67[wt%Na₂O]) + (25.88[wt%MgO]) + (5.32[wt%CaO]) − ? + ??indicates text missing or illegible when filed

In some embodiments, the target ET may be determined according to thefollowing equation:

E_(T)=(113.95[wt% SiO₂])+(0.22[wt% Al₂O₃])−(2.75[wt% B₂O₃])−(0.39[wt%CaO])−(0.94[wt% F])−(0.49[wt% MgO])−(0.47[wt% Na₂O])+113.95.

In some embodiments, the target ET may be determined according to thefollowing equation:

E_(T)=(91.49[wt% SiO₂])+(0.21[wt% Al₂O₃])−(2.67[wt% B₂O₃])+(0.15[wt%CaO])+(1.86[wt% F])−(0.16[wt% MgO])−(6.53[wt% Na₂O])+91.49.

In some embodiments, the target ET may be determined according to thefollowing equation:

E_(T) = (−10.97[wt%SiO₂]) + (3.95[wt%Al₂O₃]) − (1.97[wt%B₂O₃]) + (3.03[wt% CaO]) + (0.39[wt%F] + (0.09[wt% MgO]) − (1.6[wt%Na₂O]) − 1097.

In embodiments, the CTE_(M) of the modified glass composition is within+/−1.0×10⁻⁷/° C. of the target CTE_(T) over a corresponding temperaturerange. It should be understood that the accuracy of the CTE_(M) may varydepending on the specific linear regression used, the temperature rangeover which the CTE is measured and approximated, and the glasscomposition.

It is further contemplated that other properties may be predicted basedon linear regression modeling. For example, in embodiments, the Young'smodulus (sometimes referred to as the “elastic modulus” or “E-mod”) fora glass composition may be predicted based on linear regressionmodeling. Accordingly, one or more properties of a modified glasscomposition can be predicted prior to manufacturing a glass article fromthe glass composition. This may enable confirmation that the modifiedglass composition will meet processing requirements and that the glassarticle formed from the modified glass composition will have the desiredproperties before mixing the batch oxides and manufacturing the glassarticle.

Although the desired properties may vary depending on the particularembodiment, end use, and the processing requirements for the glasscomposition, in embodiments, the glass articles have a Young's modulusof greater than or equal to 65 GPa, which may minimize flexing of theglass during processing and prevent damage to devices attached to theglass, such as when the glass is used as a carrier substrate forelectronic devices. For example, the glass articles may have a Young'smodulus of greater than or equal to 68 GPa, greater than or equal to 70GPa, greater than or equal to 72 GPa, greater than or equal to 73 GPa,greater than or equal to 74 GPa, greater than or equal to 75 GPa,greater than or equal to 76 GPa, greater than or equal to 78 GPa,greater than or equal to 80 GPa, greater than or equal to 82 GPa,greater than or equal to 84 GPa, greater than or equal to 86 GPa,greater than or equal to 88 GPa, or greater than or equal to 90 GPa. Theglass article may have a Young's modulus of greater than or equal to 65GPa and less than or equal to 100 GPa, greater than or equal to 70 GPaand less than or equal to 100 GPa, or greater than or equal to 72 GPaand less than or equal to 85 GPa.

In embodiments, the glass composition has a 200 Poise (200 P)temperature of less than 1500° C., which may enable the glass to bemelted in a variety of processing facilities. For example, the glasscomposition may have a 200 P temperature of less than or equal to 1500°C. or less than or equal to 1450° C. In some embodiments, the glasscomposition has a 200 P temperature of greater than or equal to 1000° C.to 1500° C., greater than or equal to 1050° C. and less than or equal to1500° C., greater than or equal to 1100° C. and less than or equal to1500° C., greater than or equal to 1150° C. and less than or equal to1500° C., greater than or equal to 1200° C. and less than or equal to1500° C., greater than or equal to 1250° C. and less than or equal to1500° C., greater than or equal to 1300° C. and less than or equal to1500° C., greater than or equal to 1000° C. and less than or equal to1450° C., greater than or equal to 1050° C. and less than or equal to1450° C., greater than or equal to 1100° C. and less than or equal to1450° C., greater than or equal to 1150° C. and less than or equal to1450° C., greater than or equal to 1200° C. and less than or equal to1450° C., greater than or equal to 1250° C. and less than or equal to1450° C., or greater than or equal to 1300° C. and less than or equal to1450° C.

EXAMPLES

The following examples illustrate one or more features of theembodiments described herein.

Example 1

A base glass composition of alkali/alkaline earthzincboroaluminosilicate glass and a base glass composition ofalkali/alkaline earth boroaluminosilicate glass were selected based ontheir CTE (from 85 to 95×10⁻⁷/° C. over the range from 20° C. to 260°C.), Young's modulus (greater than 65 GPa), and ease of melting (a 200Poise temperature of less than 1500° C.). Each of the base glasscompositions were varied slightly to produce modified glasscompositions. The glass compositions were melted in covered Pt cruciblesat a temperature between 1450° C. and 1475° C., poured into patties, andannealed to form glass articles. The alkali/alkaline earthzincboroaluminosilicate glass articles were coarse ground, then melted asecond time to ensure good glass homogeneity. All glass articles werethen characterized. In particular, X-ray fluorescence (XRF) was used tocharacterize the chemical composition, the coefficient of thermalexpansion (CTE) was measured using dilatometry, and Young's modulus wasmeasured using resonant ultrasound spectroscopy (RUS). For instance, oneor more measurements may be conducted in accordance with ASTM E228and/or ASTM C623 and/or ASTM C1198-09(2013).

Tables 2 and 3 show the compositions, measured CTE, and measured Young'smodulus for the alkali/alkaline earth zincboroaluminosilicate glasscompositions, while Table 3 shows the compositions and measured CTE forthe alkali/alkaline earth boroaluminosilicate glass compositions. Forthe compositions provided in Tables 2 and 3, Composition 1 (“Comp. 1”)served as the base glass composition. Note that the CTE range from 78 to100×10⁻⁷/° C. could be obtained by replacing Na₂O with MgO, or byreplacing MgO with Na₂O. Accordingly, the data provided in Tables 2 and3 demonstrates that the CTE can be controlled by adjusting the cationfield strength.

TABLE 2 Table 2: Glasses in the Alkali/Alkaline EarthZincboroaluminosilicate glass family with CTE Values from 78-100 ×10⁻⁷/° C. and Young's Modulus >68 GPa Comp. Comp. Comp. Comp. Comp.Comp. Comp. Comp. Comp. Comp. 1 2 3 4 5 6 7 8 9 10 Oxide (wt %) measuredby XRF SiO₂ 62.8 61.5 62.9 62.9 62.9 63.0 62.8 61.0 63.4 59.7 Al₂O₃ 2.872.78 2.91 2.96 2.92 2.91 2.91 2.81 2.92 2.72 B₂O₃ 0.80 0.92 0.95 0.820.95 0.79 0.95 0.87 0.94 0.90 Na₂O 8.33 8.29 16.4 15.3 14.4 13.6 13.613.4 13.2 12.9 K₂O 9.16 9.15 0.01 0.01 0.01 0.00 0.01 0.01 0.00 0.01 MgO3.03 3.31 4.13 4.98 6.13 6.79 7.14 8.26 7.15 9.76 CaO 0.04 0.04 0.050.06 0.07 0.07 0.08 0.08 0.08 0.09 TiO₂ 0.70 0.69 0.70 0.70 0.70 0.700.69 0.68 0.70 0.67 ZnO 11.2 11.9 11.5 11.7 11.4 11.4 11.4 12.6 11.412.8 Sb₂O₃ 0.43 0.44 0.44 0.40 0.44 0.44 0.44 0.41 0.44 0.42 MeasuredCTE 99.0 97.6 93.8 88.8 84.2 83.7 82.3 81.8 81.4 80.4 (×10⁻⁷/° C.)Predicted CTE 98.8 97.8 93.1 89.2 85.9 83.5 83.0 81.8 81.3 80.2 (×10⁻⁷/°C.) Measured 69.3 69.6 70.7 73.4 72.5 74.4 73.4 74.6 76.1 75.6 Young'sModulus (GPa) Predicted 70.1 68.8 69.7 73.3 73.6 74.1 74.6 74.6 75.575.4 Young's Modulus (GPa) Predicted 200 1367 1356 1273 1326 1326 13321281 1331 1348 1301 Poise Temp. (° C.)

TABLE 3 Table 3: Glasses in the Alkali/Alkaline EarthZincboroaluminosilicate glass family with CTE Values from 78-84 × 10⁻⁷/°C. and Young's Modulus >73 GPa Comp. Comp. Comp. Comp. Comp. Comp. Comp.Comp. Comp. 11 12 13 14 15 16 17 18 19 Oxide (wt %) measured by XRF SiO₂63.38 64.19 63.53 63.07 62.66 63.46 63.23 63.05 62.69 Al₂O₃ 2.93 3.102.93 2.91 2.89 2.99 2.99 2.90 2.89 B₂O₃ 0.74 0.94 0.91 0.95 0.92 0.810.84 0.94 0.94 Na₂O 12.66 12.70 12.24 13.09 13.54 13.34 13.89 13.3413.79 K₂O 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 MgO 7.48 6.967.87 7.48 7.44 6.57 6.50 7.18 7.15 CaO 0.08 0.08 0.09 0.08 0.08 0.070.07 0.08 0.08 TiO₂ 0.70 0.70 0.70 0.69 0.69 0.69 0.68 0.69 0.69 ZnO11.27 10.82 11.25 11.45 11.36 11.56 11.44 11.40 11.41 Sb₂O₃ 0.44 0.380.44 0.44 0.44 0.42 0.42 0.44 0.44 Measured CTE 79.7 79.4 78.1 81.6 82.081.0 83.2 81.9 83.9 (×10⁻⁷/° C.) Predicted CTE 79.7 79.4 77.7 80.9 82.881.2 83.2 81.8 83.8 (× 10⁻⁷/° C.) Measured 75.3 80.0 76.3 74.5 74.6 73.573.5 74.1 74.1 Young's Modulus (GPa) Predicted 75.0 78.9 76.4 74.7 74.274.5 73.2 73.6 73.9 Young's Modulus (GPa) Predicted 200 1402 1406 13841285 1281 1280 1267 1279 1279 Poise Temp. (° C.)

For each of the glass compositions provided in Tables 2 and 3, themeasured Young's modulus values exceeded 69 GPa, while the predicted 200Poise temperature for each of the glass compositions was below 1450° C.

TABLE 4 Table 4: Glasses in the Alkali/Alkaline EarthBoroaluminosilicate glass family with CTE Values from 85-96 × 10⁻⁷/° C.Comp. 20 Comp. 21 Comp. 22 Comp. 23 Oxide (wt %) measured by XRF SiO₂64.28 64.28 63.72 63.98 Al₂O₃ 14.33 14.39 14.31 14.33 B₂O₃ 2.74 2.732.79 2.45 Li₂O 4.3 4.3 4.28 4.31 Na₂O 9 10.87 10.88 12.83 MgO 2.61 2.581.3 1.25 CaO 2.39 0.5 2.37 0.5 SnO₂ 0.36 0.36 0.37 0.35 Measured CTE 8590 91 96 (×10⁻⁷/° C.) Predicted CTE 85 89 81 96 (×10⁻⁷/° C.)

For the alkali/alkaline earth boroaluminosilicate glass compositionsshown in Table 4, the CTE values are shown for the range of 85 to96×10⁻⁷/° C. range, although compositions could have been selected toencompass the entire range from 78 to 100×10⁻⁷/° C. Because of the loweramount of MgO present in the starting glass composition (Comp. 20) ascompared to the amount of MgO in Comp. 1, both MgO and CaO replacementby Na₂O was needed to achieve the CTEs throughout the range.

The composition and property data provided in Tables 2-4 were combinedand standard linear regression analysis was used to construct apredictive model for both C and Young's modulus. The regressioncoefficients that were obtained are provided in Table 5.

TABLE 5 Table 5: Linear Regression Coefficients for CTE and Young'sModulus CTE (20° Young's Oxide C.-260° C.) Coefficient ModulusCoefficient SiO₂ Intercept −1.171629046 Intercept −228.971 Al₂O₃ XVariable 1 −1.314280351 X Variable 1 34.66347 B₂O₃ X Variable 2−0.844484203 X Variable 2 4.593175 Na₂O X Variable 3 4.364221579 XVariable 3 1.645936 MgO X Variable 4 0.97884678 X Variable 4 3.349705TiO₂ X Variable 5 47.09788707 X Variable 5 174.5979 ZnO X Variable 6−0.645462742 X Variable 6 2.703049 K₂O X Variable 7 4.45477385 XVariable 7 2.123741 CaO X Variable 8 −37.20821358 X Variable 8 5.121629

The predicted results from these linear regression models are providedin Tables 2-4 above. In all cases, the predicted values for CTE arewithin 1.0×10⁻⁷/° C. and the predicted values for Young's modulus arewithin 1.0 GPa. The agreement between the measured and predicted valuesis shown in FIGS. 4 and 5 . Specifically, FIG. 4 is a plot of themeasured CTE (Y-axis; values x 10⁻⁷/° C.) as a function of the predictedCTE (X-axis; values x 10⁻⁷/° C.) for the glasses from Tables 2 and 3.FIG. 5 is a plot of the measured Young's modulus (Y-axis; in GPa) as afunction of the predicted Young's modulus (X-axis; in GPa). As may beseen from the R² value for both of FIGS. 4 and 5 , the model has a highpredictive capability for both CTE and Young's modulus over the CTErange from 78-100×10⁻⁷/° C. measured from 20° C. to 260° C.

In order to confirm the utility of the model for manufacturing a glasswith a target CTE_(T), a week-long trial was conducted in which theamounts of Na₂O and MgO were varied. Minor variations in other oxidecomponents are related to issues such as the need to overcompensate forparticular components due to raw material losses during batching or toselective volatilization losses during melting. The compositions andpredicted CTEs are reported in Table 6. For each of the glasscompositions, the predicted CTE was in the range from 84 to 93×10⁻⁷/° C.from 20° C. to 260° C. and the predicted Young's modulus was greaterthan 65 GPa based on the regression coefficients provided in Table 4.

TABLE 6 Table 6: Glasses made in production tank with predicted CTEvalues Oxide (wt %) measured by XRF Predicted CTE SiO₂ Al₂O₃ B₂O₃ Na₂OMgO TiO₂ ZnO K₂O CaO Sb₂O₃ (×10⁻⁷/° C.) Comp. 24 62.66 2.97 0.94 14.176.66 0.69 11.30 0.16 0.04 0.41 87 Comp. 25 62.61 2.98 0.94 14.19 6.680.69 11.30 0.15 0.04 0.42 87 Comp. 26 62.59 2.98 0.96 14.23 6.68 0.6911.28 0.14 0.04 0.41 87 Comp. 27 62.67 2.99 0.94 14.17 6.67 0.69 11.290.14 0.04 0.41 87 Comp. 28 62.63 2.87 0.92 14.66 6.37 0.70 11.39 0.020.02 0.42 89 Comp. 29 62.60 2.87 0.95 14.66 6.35 0.70 11.41 0.02 0.020.42 89 Comp. 30 62.69 2.87 0.93 14.63 6.33 0.70 11.39 0.02 0.02 0.42 89Comp. 31 62.74 2.87 0.93 14.60 6.34 0.69 11.37 0.02 0.02 0.42 89 Comp.32 62.7 2.88 0.93 14.66 6.32 0.69 11.36 0.02 0.02 0.42 89 Comp. 33 62.762.87 0.92 14.62 6.32 0.70 11.35 0.02 0.02 0.42 89 Comp. 34 62.80 2.870.92 14.62 6.28 0.69 11.36 0.02 0.02 0.42 89 Comp. 35 62.82 2.86 0.9214.74 6.19 0.69 11.33 0.02 0.02 0.41 89 Comp. 36 62.86 2.86 0.93 14.656.24 0.69 11.32 0.02 0.02 0.41 89 Comp. 37 62.81 2.85 0.94 14.71 6.210.69 11.33 0.02 0.02 0.42 89 Comp. 38 62.91 2.87 0.93 14.65 6.19 0.6911.31 0.02 0.02 0.41 89 Comp. 39 62.72 2.86 0.95 14.76 6.21 0.69 11.350.02 0.02 0.42 89 Comp. 40 62.76 2.86 0.94 14.79 6.18 0.69 11.33 0.020.02 0.41 90 Comp. 41 62.74 2.96 0.94 14.20 6.75 0.69 11.27 0.02 0.020.41 87 Comp. 42 62.82 2.90 0.93 14.59 6.33 0.69 11.29 0.02 0.02 0.41 89Comp. 43 62.63 2.90 0.98 14.11 6.96 0.69 11.28 0.02 0.02 0.41 87 Comp.44 62.74 2.88 0.93 14.08 6.95 0.69 11.28 0.02 0.02 0.41 87 Comp. 4562.71 2.87 0.93 14.15 6.89 0.69 11.30 0.02 0.02 0.42 87 Comp. 46 62.622.88 0.94 14.20 6.88 0.69 11.32 0.02 0.03 0.42 87 Comp. 47 62.59 2.881.02 14.20 6.85 0.69 11.30 0.02 0.03 0.42 87 Comp. 48 62.67 2.90 0.9514.17 6.86 0.69 11.30 0.03 0.03 0.41 87 Comp. 49 63.08 2.91 0.93 13.547.16 0.69 11.23 0.02 0.03 0.41 85 Comp. 50 62.78 2.91 0.93 13.35 7.560.69 11.32 0.02 0.03 0.41 84 Comp. 51 62.79 2.88 0.92 13.34 7.59 0.6911.33 0.02 0.03 0.42 84 Comp. 52 62.77 2.88 0.93 13.37 7.58 0.69 11.330.02 0.02 0.41 84 Comp. 53 62.77 2.87 0.94 13.40 7.56 0.69 11.32 0.020.02 0.41 85 Comp. 54 62.81 2.88 0.92 13.39 7.55 0.69 11.31 0.02 0.020.41 85 Comp. 55 62.78 2.88 0.92 13.43 7.53 0.69 11.31 0.02 0.02 0.42 85Comp. 56 62.83 2.90 0.91 13.42 7.51 0.69 11.29 0.02 0.02 0.41 85 Comp.57 62.86 2.88 0.90 13.45 7.48 0.69 11.29 0.02 0.02 0.41 85 Comp. 5862.82 2.94 0.93 13.45 7.43 0.69 11.29 0.02 0.02 0.4 85 Comp. 59 62.962.97 0.91 13.51 7.28 0.68 11.27 0.02 0.02 0.41 84 Comp. 60 62.86 2.960.94 13.54 7.31 0.69 11.25 0.02 0.02 0.41 85 Comp. 61 63.21 2.86 0.9215.71 4.93 0.69 11.24 0.02 0.02 0.41 92 Comp. 62 63.36 2.84 0.91 15.904.62 0.68 11.25 0.02 0.02 0.41 93

Example 2

Another base glass composition was selected based on their CTE (from 40to 70×10⁻⁷/° C. over the range from 20° C. to 260° C.), Young's modulus(greater than 72 GPa), and ease of melting (a 200 Poise temperature ofless than 1500° C.). The glass compositions were prepared as describedabove. Tables 7 and 8 show the compositions, measured CTE, and measuredYoung's modulus for the glass compositions.

TABLE 7 Table 7: Adjustable Glass Compositions with CTE in the range of40-70 × 10⁻⁷/° C. (Reported in Oxide wt %) SiO₂ Al₂O₃ B₂O₃ Na₂O MgO CaOSb₂O₃ SnO₂ Comp. 63 49.70 24.94 9.76 3.22 3.46 8.13 0.57 0.00 Comp. 6448.93 24.90 10.33 3.58 3.15 8.47 0.00 0.21 Comp. 65 48.91 24.95 10.283.56 3.17 8.44 0.00 0.21 Comp. 66 49.81 24.94 9.68 3.85 2.80 8.14 0.570.00 Comp. 67 49.07 24.93 10.05 3.69 3.06 8.43 0.00 0.21 Comp. 68 49.1925.16 9.57 5.10 1.57 8.58 0.00 0.20 Comp. 69 49.56 25.33 9.01 4.99 1.648.65 0.00 0.19 Comp. 70 49.39 25.05 9.52 5.75 0.81 8.53 0.00 0.20 Comp.71 49.39 25.04 9.77 6.30 0.36 8.50 0.00 0.20 Comp. 72 49.09 24.99 9.866.77 0.13 8.37 0.00 0.20 Comp. 73 48.88 25.03 9.71 6.83 0.26 8.41 0.000.20 Comp. 74 49.13 25.01 9.84 6.73 0.09 8.38 0.00 0.20 Comp. 75 47.3725.12 9.82 7.43 1.10 8.45 0.00 0.20 Comp. 76 47.62 25.44 9.11 7.54 1.218.39 0.00 0.20 Comp. 77 47.46 25.35 9.29 7.50 1.20 8.39 0.00 0.20 Comp.78 43.86 24.93 9.80 5.33 5.26 10.17 0.52 0.00 Comp. 79 43.87 25.45 14.785.30 2.38 7.46 0.51 0.00

TABLE 8 Table 8: Measured and Predicted Properties of Adjustable GlassCompositions with CTE in the range of 40-70 × 10⁻⁷/° C. Modeled MeasuredModeled Measured Young's Young's CTE < Tg CTE Modulus Modulus (×10⁻⁷/°C.) (×10⁻⁷/° C.) (GPa) (GPa) Comp. 63 47.0 47.5 80 80 Comp. 64 48.7 47.778 78 Comp. 65 48.5 48.0 78 78 Comp. 66 49.1 49.1 79 79 Comp. 67 49.049.9 78 78 Comp. 68 53.6 52 75 76 Comp. 69 53.2 53.8 76 76 Comp. 70 55.756.1 74 74 Comp. 71 57.6 58.3 72 72 Comp. 72 59.3 58.8 72 72 Comp. 7359.7 59.3 72 72 Comp. 74 59.1 59.9 72 72 Comp. 75 63.0 62.6 74 74 Comp.76 63.3 63.1 75 75 Comp. 77 63.2 63.4 75 75 Comp. 78 59.7 59.9 83 83Comp. 79 54.3 54.4 74 74

Standard linear regression analysis was used to construct a predictivemodel for both CTE and Young's modulus based on the composition andproperty data provided in Tables 7-8. The regression coefficients thatwere obtained are provided in Table 8.

TABLE 9 Table 9: Linear Regression Coefficients for CTE and Young'sModulus CTE (20° Young's Oxide C.-260° C.) Coefficient ModulusCoefficient SiO₂ Intercept 31.98615022 Intercept 119.6278898 Al₂O₃ XVariable 1 −0.430953446 X Variable 1 −0.724461839 B₂O₃ X Variable 20.061922264 X Variable 2 −1.752943291 Na₂O X Variable 3 4.247079525 XVariable 3 −0.094245376 MgO X Variable 4 0.904545076 X Variable 42.199434789 CaO X Variable 5 1.026704946 X Variable 5 −1.43091694

The predicted results from these linear regression models are providedin Table 8 above. In all cases, the predicted values for CTE are within1.6×10⁻⁷/° C., with all but one predicted value being within 1.0×10⁻⁷/°C., and the predicted values for Young's modulus are within 1.0 GPa. Theagreement between the measured and predicted values is shown in FIGS. 6and 7 . Specifically, FIG. 6 is a plot of the measured CTE (Y-axis;values x 10⁻⁷/° C.) as a function of the predicted CTE (X-axis; values x10⁻⁷/° C.) for the glasses from Table 7. FIG. 7 is a plot of themeasured Young's modulus (Y-axis; in GPa) as a function of the predictedYoung's modulus (X-axis; in GPa). As may be seen from the R² value forboth of FIGS. 6 and 7 , the model has a high predictive capability forboth CTE and Young's modulus over the CTE range from 40-70×10⁻⁷/° C.measured from 20° C. to 260° C.

Using the models described in Table 9, CTEs and Young's modulus valuesfor additional various glass compositions were predicted. In particular,Comp. 80 below was used as a base glass composition to generate variousadditional glass compositions. The compositions are provided in Table10, and predicted values of various properties are provided in Table 11.

TABLE 10 Table 10: Adjustable Glass Compositions with CTE in the rangeof 40-70 × 10⁻⁷/° C. (Reported in Oxide wt %) SiO₂ Al₂O₃ b₂o₃ Na₂O MgOCaO F Sb₂O₃ Comp. 80 49.95 25.00 9.83 0.00 6.72 8.34 0.00 0.50 Comp. 8149.95 25.00 9.83 0.00 4.72 10.34 0.00 0.50 Comp. 82 49.95 25.00 9.831.51 5.20 8.34 0.00 0.50 Comp. 83 49.95 25.00 9.83 1.88 4.84 8.34 0.000.50 Comp. 84 49.95 25.00 9.83 2.25 4.46 8.34 0.00 0.50 Comp. 85 49.9525.00 9.83 3.10 3.61 8.34 0.00 0.50 Comp. 86 49.95 25.00 9.83 3.35 3.368.34 0.00 0.50 Comp. 87 49.95 25.00 9.83 3.35 3.36 8.34 1.15 0.50 Comp.88 49.95 25.00 9.83 4.00 2.71 8.34 0.00 0.50 Comp. 89 49.95 25.00 9.834.00 2.71 8.34 1.15 0.50 Comp. 90 49.95 25.00 9.83 5.25 1.47 8.34 0.000.50 Comp. 91 49.95 25.00 9.83 5.35 1.37 8.34 0.00 0.50 Comp. 92 49.9525.00 9.83 5.51 1.20 8.34 0.00 0.50 Comp. 93 49.95 25.00 9.83 6.26 0.458.34 0.00 0.50 Comp. 94 49.95 25.00 9.83 6.46 0.25 8.34 0.00 0.50 Comp.95 49.95 25.00 9.83 6.71 0.00 8.34 0.00 0.50 Comp. 96 47.95 25.00 9.837.52 1.20 8.34 0.00 0.50 Comp. 97 47.95 25.00 9.83 7.52 1.20 8.34 1.000.50 Comp. 98 47.95 25.00 9.83 7.52 1.20 8.34 1.50 0.50

TABLE 11 Table 11: Predicted Properties of Adjustable Glass Compositionswith CTE in the range of 40-70 × 10⁻⁷/° C. Modeled Predicted PredictedModeled Young's Predicted 200 Poise Liquidus CTE < Tg Modulus DensityTemperature Temperature (×10⁻⁷/° C.) (GPa) (g/cm³) (° C.) (° C.) Comp.80 37 82 3 1446 1269 Comp. 81 39 81 3 1446 1200 Comp. 82 41 81 3 14831215 Comp. 83 43 80 3 1460 1147 Comp. 84 45 80 3 1437 1185 Comp. 85 4679 2 1482 1148 Comp. 86 48 78 2 1487 1122 Comp. 87 48 — — — — Comp. 8851 77 2 1492 1231 Comp. 89 51 — — — — Comp. 90 53 77 2 1467 1230 Comp.91 56 76 2 1487 1228 Comp. 92 57 76 2 1482 1228 Comp. 93 59 75 2 14441223 Comp. 94 66 75 2 1454 1222 Comp. 95 60 74 2 1467 1163 Comp. 96 7174 2 1467 1063 Comp. 97 71 — — — — Comp. 98 71 — — — —

As shown in Table 11, each of the glass compositions is expected to havea CTE between 40×10⁻⁷/° C. and 60×10⁻⁷/° C., a Young's modulus greaterthan 72 GPa, and a 200 Poise temperature of less than 1500° C.

To further confirm that the concept could be used for a variety ofglasses and to achieve a variety of CTEs, different starting glasscompositions were studied. Two modeled glass compositions were selectedto cover CTE_(TS) in the range below 60×10⁻⁷/° C., and the CTE wasmodeled using the linear regression model provided in Table 8. Theresults are provided in Table 12 below.

TABLE 12 Table 12: Adjustable Glass Compositions with Modeled CTE in therange of 41-60 × 10⁻⁷/° C. Starting Replacing MgO Glass Replacing Na₂Ofor MgO for Na₂O Comp. Comp. Comp. Comp. Comp. Comp. Comp. Comp. Comp.Comp. Comp. Oxide (wt %) 99 100 101 102 103 104 105 106 107 108 109 SiO₂49.95 49.95 54.1 50 50 50 50 50 50 50 50 Al₂O₃ 25 25 22.9 25 25 25 25 2525 25 25 B₂O₃ 9.83 9.83 9 9.8 9.8 9.8 9.8 9.8 9.8 9.8 9.8 Na₂O 5.51 1.511.7 3.1 3.3 3.4 4 5.3 5.4 6.3 6.7 MgO 1.2 5.2 4.4 3.6 3.4 3.3 2.7 1.51.4 0.4 0 CaO 8.34 8.34 7.6 8.3 8.3 8.3 8.4 8.3 8.3 8.3 8.4 SnO₂ 0.160.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 Modeled CTE < Tg 57 4143 46 48 49 51 53 56 59 60 (×10⁻⁷/° C.) Modeled Young's 76.4 80.9 80.378.9 78.4 78 77.5 76.5 75 75.1 74.4 Modulus (GPa) Modeled Density 2.452.51 2.51 2.49 2.49 2.49 2.48 2.45 2.44 2.45 2.45 (g/cm³) Modeled 200Poise 1482 1483 1460 1482 1487 1485 1492 1467 1487 1444 1467 Temp (° C.)Modeled Liquidus 1228 1215 1147 1148 1121 1303 1230 1230 1227 1223 1162Temp (° C.)

Based on the modeled data, the CTE can be tuned within the range from 40to 60×10⁻⁷/° C. by starting with different base glass compositions andadjusting the composition. Each of the compositions had a CTE within thetarget range, a Young's modulus of greater than 72 GPa and a 200 Poisetemperature of less than 1500° C., indicating that these glasses wouldremain suitable for processing under the same or similar conditions asthe base glass composition.

Using the models described in Table 9, CTEs and Young's modulus valuesfor glass compositions modified from a different base glass compositionwere predicted. In particular, Comp. 110 below was modified to generatevarious additional glass compositions. The compositions are provided inTable 13, and predicted values of various properties are provided inTable 14.

TABLE 13 Table 13: Adjustable Glass Compositions with CTE in the rangeof 40-60 × 10⁻⁷/° C. (Reported in Oxide wt %) SiO₂ Al₂O₃ Na₂O K₂O MgOCaO La₂O₃ Sb₂O₃ Comp. 110 46.12 18.49 0.00 0.00 3.77 1.44 30.02 0.00Comp. 111 46.12 18.49 0.00 0.00 3.77 6.44 25.02 0.00 Comp. 112 39.5018.49 0.00 4.54 0.00 7.42 30.02 0.00 Comp. 113 39.50 18.49 0.00 5.040.00 6.92 30.02 0.00 Comp. 114 39.50 18.49 0.00 5.54 0.00 6.42 30.020.00 Comp. 115 39.50 18.49 0.00 5.78 0.00 6.18 30.02 0.00 Comp. 11639.50 18.49 0.00 6.78 0.00 5.18 30.02 0.00 Comp. 117 39.50 18.49 3.530.00 0.00 8.42 30.02 0.00 Comp. 118 39.50 18.49 3.53 0.50 0.00 7.2 30.020.00 Comp. 119 39.50 18.49 1.77 5.77 0.00 4.42 30.02 0.00 Comp. 12039.50 18.49 2.77 4.77 0.00 4.42 30.02 0.00 Comp. 121 39.50 18.49 4.030.00 0.00 7.92 30.02 0.00 Comp. 122 39.50 18.49 3.77 3.77 0.00 4.4230.02 0.00

TABLE 14 Table 14: Predicted Properties of Adjustable Glass Compositionswith CTE in the range of 40-60 × 10⁻⁷/° C. Modeled Predicted PredictedModeled Young's Predicted 200 Poise Liquidus CTE < Tg Modulus DensityTemperature Temperature (×10⁻⁷/° C.) (GPa) (g/cm³) (° C.) (° C.) Comp.110 42 96 3.16 1452 1188.7 Comp. 111 43 94 3.07 1469 1259.7 Comp. 112 4593 3.18 1462 1194.9 Comp. 113 46 93 3.17 1463 1200.2 Comp. 114 48 933.17 1462 1186.0 Comp. 115 49 93 3.19 1462 1183.0 Comp. 116 50 93 3.191458 1182.5 Comp. 117 51 94 3.20 1440 1194.8 Comp. 118 52 93 3.19 14571166.6 Comp. 119 53 93 3.18 1463 1164.0 Comp. 120 55 92 3.18 1460 1157.3Comp. 121 56 93 3.19 1445 1125.9 Comp. 122 58 90 3.16 1416 1138.0

As shown in Table 14, each of the glass compositions is expected to havea CTE between 40×10⁻⁷/° C. and 60×10⁻⁷/° C., a Young's modulus greaterthan 90 GPa, and a 200 Poise temperature of less than 1500° C.

Example 3

In order to achieve higher CTEs, a glass composition including Li₂O wasstudied. In particular, Comp. 123 below was modified to generateadditional glass compositions having CTEs between 90×10⁻⁷/° C. and130×10⁻⁷/° C. The compositions are provided in Table 15, and predictedvalues of various properties are provided in Table 16.

TABLE 15 Table 15: Adjustable Glass Compositions with CTE in the rangeof 90-130 × 10⁻⁷/° C. (Reported in Oxide wt %) SiO₂ Al₂O₃ Li₂O Na₂O K₂OMgO CaO Sb₂O₃ Comp. 123 65.96 11.55 6.20 7.54 0.36 1.27 6.83 0.25 Comp.124 65.96 11.55 6.2 9.54 0.36 1.27 4.83 0.25 Comp. 125 65.96 11.55 6.211.54 0.36 1.27 2.83 0.25 Comp. 126 65.96 11.55 5.2 10.54 5.36 0.27 0.820.25 Comp. 127 65.96 11.55 7.2 10.54 3.36 0.27 0.83 0.25 Comp. 128 65.9611.55 3.2 17.54 0.36 0.27 0.83 0.25 Comp. 129 62.6 9.55 9.2 10.00 8.36 00 0.25 Comp. 130 62.6 9.55 3.2 11.00 13.36 0 0 0.25 Comp. 131 62.6 9.556.2 12.00 9.36 0 0 0.25 Comp. 132 62.6 9.55 3.2 14.73 9.36 0.27 0 0.25Comp. 133 60.6 9.55 3.2 13.00 13.36 0 0 0.25 Comp. 134 59.6 9.55 3.214.00 13.36 0 0 0.25 Comp. 135 58.6 9.55 3.2 15.00 13.36 0 0 0.25 Comp.136 57.1 9.55 3.2 16.50 13.36 0 0 0.25

TABLE 16 Table 16: Predicted Properties of Adjustable Glass Compositionswith CTE in the range of 90-130 × 10⁻⁷/° C. Modeled Predicted PredictedModeled Young's Predicted 200 Poise Liquidus CTE <Tg Modulus DensityTemperature Temperature (×10⁻⁷/° C.) (GPa) (g/cm³) (° C.) (° C.) Comp.123 92 83 2.49 1340 901.93 Comp. 124 95 83 2.48 1341 855.03 Comp. 125 9882 2.47 1278 794.94 Comp. 126 102 82 2.45 1388 759.21 Comp. 127 103 822.45 1266 809.78 Comp. 128 106 74 2.46 1484 781.26 Comp. 129 109 83 2.481268 877.35 Comp. 130 115 75 2.46 1364 974.46 Comp. 131 117 81 2.47 1303741.1 Comp. 132 119 75 2.47 1403 935.18 Comp. 133 121 72 2.47 1440 726.7Comp. 134 123 72 2.49 1404 763.69 Comp. 135 128 77 2.48 1406 779.49Comp. 136 131 77 2.5 1394 752.21

Standard linear regression analysis was used to construct a predictivemodel for both CTE and Young's modulus based on the compositionsprovided in Table 15 and corresponding measured properties. Theregression coefficients that were obtained are provided in Table 17.

TABLE 17 Table 17: Linear Regression Coefficients for CTE and Young'sModulus CTE (20° Young's Oxide C.-260° C.) Coefficient ModulusCoefficient SiO₂ Intercept 137.5612129 Intercept 72.03447013 Al₂O₃ XVariable 1 −5.471592999 X Variable 1 0.096444782 Li₂O X Variable 21.181240915 X Variable 2 0.92453515 Na₂O X Variable 3 2.221133922 XVariable 3 0.092136596 K₂O X Variable 4 1.319063347 X Variable 4−0.464253215 MgO X Variable 5 −5.372521274 X Variable 5 −1.197632544 CaOX Variable 6 −0.097587446 X Variable 6 1.117490089

The predicted results from these linear regression models are providedin Table 16 above. As shown in Table 16, each of the glass compositionsis expected to have a CTE between 90×10⁻⁷/° C. and 130×10⁻⁷/° C., aYoung's modulus greater than 72 GPa, and a 200 Poise temperature of lessthan 1500° C. The agreement between the measured and predicted values isshown in FIGS. 8 and 9 . Specifically, FIG. 8 is a plot of the measuredCTE (Y-axis; values x 10⁻⁷/° C.) as a function of the predicted CTE(X-axis; values x 10⁻⁷/° C.) for the glasses from Table 16. FIG. 9 is aplot of the measured Young's modulus (Y-axis; in GPa) as a function ofthe predicted Young's modulus (X-axis; in GPa). As may be seen from theR² value for both of FIGS. 8 and 9 , the model has a high predictivecapability for both CTE and Young's modulus over the CTE range from90-130×10⁻⁷/° C. measured from 20° C. to 260° C.

Additional compositions were studied to explore the ability to adjustthe CTE over a wider range of temperatures. In particular, previousexperiments observed the CTE over the range from 20° C. to 260° C.Additional glass compositions having CTEs between 90×10⁻⁷/° C. and150×10⁻⁷/° C. measured over 20° C. to 300° C. and 20° C. to 390° C. areprovided in Table 18, and predicted values of CTE over various rangesare provided in Table 19.

TABLE 18 Table 18: Adjustable Glass Compositions with CTE in the rangeof 90-150 × 10⁻⁷/° C. over 20° C. to 300° C. and 20° C. to 390° C.(Reported in Oxide wt %) SiO₂ Al₂O₃ Li₂O Na₂O K₂O MgO CaO Sb₂O₃ Comp.137 65.73 11.55 6.02 7.3 0.34 1.34 6.62 0.51 Comp. 138 65.82 11.57 6.0311.18 0.35 1.3 2.74 0.51 Comp. 139 65.89 11.61 6.98 10.2 3.02 0.29 0.820.5 Comp. 140 63.28 9.65 8.74 9.54 7.47 0.012 0.026 0.49 Comp. 141 63.449.62 3.16 10.62 12 0.007 0.025 0.47 Comp. 142 6.303 9.7 6.12 11.65 8.440.009 0.026 0.48 Comp. 143 61.5 9.63 3.13 12.47 11.99 0.01 0.026 0.46Comp. 144 59.64 9.66 3.12 14.37 11.98 0.01 0.026 0.46 Comp. 145 58.299.67 3.11 15.69 12 0.008 0.029 0.45

TABLE 19 Table 19: Properties of Adjustable Glass Compositions with CTEin the range of 90-150 × 10⁻⁷/° C. over 20° C. to 300° C. and 20° C. to390° C. Measured Predicted Measured Predicted CTE (20° CTE (20° CTE (20°CTE (20° C.-300° C.) C.-300° C.) C.-390° C.) C.-390° C.) Comp. 137 9292.29 96.8 96.79 Comp. 138 102 101.62 107.2 107.22 Comp. 139 110 109.58115 114.98 Comp. 140 129 128.46 134.8 134.75 Comp. 141 128 130.06 132.4134.74 Comp. 142 131 130.88 137.1 137.19 Comp. 143 136 134.22 141.8139.66 Comp. 144 142 138.43 148.4 144.65 Comp. 145 139 141.46 144.7148.22

Standard linear regression analysis was used to construct a predictivemodel for CTE over 20° C. to 300° C. and over 20° C. to 390° C. based onthe compositions provided in Table 18 and corresponding measuredproperties. The regression coefficients that were obtained are providedin Table 20.

TABLE 20 Table 20: Linear Regression Coefficients for CTE over 20° C. to300° C. and 20° C. to 390° C. CTE (20° CTE (20° Oxide C.-300° C.)Coefficient C.-390° C.) Coefficient SiO₂ Intercept 131.9093419 Intercept138.5093769 Al₂O₃ X Variable 1 −5.053570424 X Variable 1 −5.655734141Li₂O X Variable 2 1.397804857 X Variable 2 1.673991001 Na₂O X Variable 32.312944293 X Variable 3 2.731779214 K₂O X Variable 4 1.485189419 XVariable 4 1.36455255 MgO X Variable 5 −4.972563994 X Variable 5−5.519456652 CaO X Variable 6 −0.05878923 X Variable 6 0.078265306

The predicted results from these linear regression models are providedin Table 19 above. As shown in Table 19, each of the glass compositionsis expected to have a CTE between 90×10⁻⁷/° C. and 150×10⁻⁷/° C. Theagreement between the measured and predicted values is shown in FIGS. 10and 11 . Specifically, FIG. 10 is a plot of the measured CTE (Y-axis;values x 10⁻⁷/° C.) as a function of the predicted CTE (X-axis; values x10⁻⁷/° C.) over 20° C. to 300° C. for the glasses from Table 18. FIG. 11is a plot of the measured CTE (Y-axis; values x 10⁻⁷/° C.) as a functionof the predicted CTE (X-axis; values x 10⁻⁷/° C.) over 20° C. to 390° C.for the glasses from Table 18. As may be seen from the R² value for bothof FIGS. 10 and 11 , the model has a high predictive capability for CTEfrom 90-150×10⁻⁷/° C. measured from 20° C. to 300° C. and from 20° C. to390° C.

Example 4

Additional compositions were studied to explore the ability to adjustthe CTE over a wider range of temperatures. In particular, previousexperiments observed the CTE over the range from 20° C. to 260° C.Additional glass compositions having CTEs between 40×10⁻⁷/° C. and70×10⁻⁷/° C. measured over 20° C. to 300° C. and 20° C. to 390° C. areprovided in Table 21, and predicted CTE values are provided in Table 22.

TABLE 21 Table 21: Adjustable Glass Compositions with CTE in the rangeof 40-70 × 10⁻⁷/° C. over 20° C. to 300° C. and 20° C. to 390° C.(Reported in Oxide wt %) SiO₂ Al₂O₃ B₂O₃ Na₂O MgO CaO Sb₂O₃ SnO₂ Comp.146 49.7 24.94 9.76 3.22 3.46 8.13 0.57 0 Comp. 147 49.7 29.94 9.76 3.223.46 8.13 0.57 0 Comp. 148 48.93 24.9 10.33 3.581 3.152 8.47 0.00 0.21Comp. 149 48.91 24.95 10.28 3.56 3.17 8.44 0.00 0.21 Comp. 150 49.8124.94 9.68 3.85 2.8 8.14 0.57 0 Comp. 151 49.81 24.94 9.68 3.85 2.8 8.140.57 0 Comp. 152 49.07 24.93 10.05 3.69 3.06 8.43 0.00 0.21 Comp. 15349.19 25.16 9.57 5.102 1.573 8.58 0.00 0.2 Comp. 154 49.56 25.33 9.014.99 1.64 8.65 0.00 0.19 Comp. 155 49.39 25.05 9.52 5.75 0.81 8.53 0.000.2 Comp. 156 49.39 25.04 9.77 6.296 0.358 8.5 0.00 0.2 Comp. 157 49.0924.99 9.86 6.77 0.13 8.37 0.00 0.203 Comp. 158 48.88 25.03 9.71 6.830.26 8.41 0.00 0.203 Comp. 159 49.13 25.01 9.84 6.73 0.093 8.38 0.000.204 Comp. 160 47.37 25.12 9.82 7.43 1.1 8.45 0.00 0.2 Comp. 161 47.6225.44 9.11 7.54 1.21 8.39 0.00 0.2 Comp. 162 47.46 25.34 9.29 7.4981.196 8.39 0.00 0.199 Comp. 163 43.86 24.93 9.8 5.33 5.26 10.17 0.52 0Comp. 164 43.87 25.45 14.78 5.3 2.38 7.46 0.51 0 Comp. 165 49.73 24.879.79 0.02 6.74 8.17 0.52 0 Comp. 166 49.75 24.88 9.8 1.41 5.255 8.160.515 0 Comp. 167 49.82 24.88 9.8 1.78 4.88 8.15 0.52 0 Comp. 168 49.6325.01 9.8 2.14 4.54 8.22 0.52 0 Comp. 169 49.7 24.96 9.8 2.97 3.7 8.190.51 0 Comp. 170 49.25 24.92 9.57 6.47 0.19 8.46 0 0.2 Comp. 171 49.4425.2 9.15 4.38 2.25 8.6 0 0.2

TABLE 22 Table 22: Properties of Adjustable Glass Compositions with CTEin the range of 40-70 × 10⁻⁷/° C. over 20° C. to 300° C. and 20° C. to390° C. Measured Predicted Measured Predicted CTE (20° CTE (20° CTE (20°CTE (20° C.-300° C.) C.-300° C.) C.-390° C.) C.-390° C.) Comp. 146 4848.8 49 50.99 Comp. 147 49 48.5 50 49.54 Comp. 148 49 49.9 50 51.56Comp. 149 49 49.9 49 51.53 Comp. 150 50 50.6 51 52.62 Comp. 151 50 50.651 52.62 Comp. 152 51 50.3 52 52.02 Comp. 153 52 54.4 54 55.66 Comp. 15454 54.1 55 55.43 Comp. 155 57 56.1 58 57.25 Comp. 156 59 57.7 61 58.77Comp. 157 60 59.4 61 60.51 Comp. 158 60 59.8 62 61.03 Comp. 159 61 59.262 60.27 Comp. 160 63 63.5 65 65.03 Comp. 161 64 64.2 65 65.97 Comp. 16264 64.0 66 65.71 Comp. 163 61 60.7 62 62.00 Comp. 164 55 54.9 57 56.30Comp. 165 42 39.7 43 42.67 Comp. 166 44 43.6 45 46.17 Comp. 167 45 44.756 47.14 Comp. 168 46 45.7 47 48.04 Comp. 169 47 48.1 49 50.25 Comp. 17059 58.3 60 59.39 Comp. 171 53 52.3 54 53.83

Standard linear regression analysis was used to construct a predictivemodel for CTE over 20° C. to 300° C. and over 20° C. to 390° C. based onthe compositions provided in Table 21 and corresponding measuredproperties. The regression coefficients that were obtained are providedin Table 23.

TABLE 23 Table 23: Linear Regression Coefficients for CTE over 20° C. to300° C. and 20° C. to 390° C. CTE (20° CTE (20° Oxide C.-300° C.)Coefficient C.-390° C.) Coefficient SiO₂ Intercept 31.86272 Intercept47.81324443 Al₂O₃ X Variable 1 −0.06728 X Variable 1 −0.28850455 B₂O₃ XVariable 2 −0.2062 X Variable 2 −0.442997258 Na₂O X Variable 3 4.215118X Variable 3 4.387516515 MgO X Variable 4 1.336897 X Variable 41.751246324 CaO X Variable 5 0.301558 X Variable 5 −0.675842501

The predicted results from these linear regression models are providedin Table 22 above. As shown in Table 22, each of the glass compositionsis expected to have a CTE between 40×10⁻⁷/° C. and 70×10⁻⁷/° C. Theagreement between the measured and predicted values is shown in FIGS. 12and 13 . Specifically, FIG. 12 is a plot of the measured CTE (Y-axis;values x 10⁻⁷/° C.) as a function of the predicted CTE (X-axis; values x10⁻⁷/° C.) over 20° C. to 300° C. for the glasses from Table 21. FIG. 13is a plot of the measured CTE (Y-axis; values x 10⁻⁷/° C.) as a functionof the predicted CTE (X-axis; values x 10⁻⁷/° C.) over 20° C. to 390° C.for the glasses from Table 21. As may be seen from the R² value for bothof FIGS. 12 and 13 , the model has a high predictive capability for CTEfrom 40-70×10⁻⁷/° C. measured from 20° C. to 300° C. and from 20° C. to390° C.

Additional glass compositions having CTEs between 80×10⁻⁷/° C. and100×10⁻⁷/° C. measured over 20° C. to 300° C. and 20° C. to 390° C. areprovided in Table 24, and predicted CTE values are provided in Table 25.

TABLE 24 Table 24: Adjustable Glass Compositions with CTE in the rangeof 80-100 × 10⁻⁷/° C. over 20° C. to 300° C. and 20° C. to 390° C.(Reported in Oxide wt %) SiO₂ Al₂O₃ B₂O₃ Na₂O K₂O MgO CaO TiO₂ ZnO Sb₂O₃Comp. 172 62.77 2.87 0.8 8.33 9.16 3.03 0.04 0.7 11.15 0.43 Comp. 17361.45 2.78 0.92 8.29 9.15 3.31 0.041 0.69 11.98 0.44 Comp. 174 62.962.913 0.95 16.35 0.01 4.125 0.051 0.695 11.45 0.44 Comp. 175 62.9 2.960.82 15.31 0.01 4.98 0.06 0.7 11.64 0.4 Comp. 176 62.93 2.923 0.95 14.410.009 6.127 0.068 0.695 11.44 0.44 Comp. 177 63.01 2.91 0.79 13.64 06.79 0.07 0.7 11.38 0.44 Comp. 178 62.84 2.905 0.95 13.59 0.01 7.1440.075 0.693 11.42 0.438 Comp. 179 61.03 2.81 0.87 13.42 0.009 8.2550.081 0.676 12.57 0.407 Comp. 180 63.42 2.92 0.94 13.16 0 7.15 0.08 0.711.35 0.44 Comp. 181 59.69 2.72 0.9 12.86 0.009 9.76 0.09 0.671 12.770.417 Comp. 182 63.38 2.93 0.74 12.66 0.01 7.48 0.08 0.7 11.27 0.44Comp. 183 64.19 3.1 0.94 12.7 0.01 6.96 0.075 0.7 10.82 0.38 Comp. 18463.53 2.93 0.91 12.24 0.01 7.87 0.09 0.7 11.25 0.44 Comp. 185 63.07 2.910.95 13.09 0.009 7.48 0.078 0.69 11.45 0.44 Comp. 186 62.66 2.89 0.9413.54 0.009 7.44 0.08 0.69 11.36 0.44 Comp. 187 63.46 2.99 0.87 13.340.009 6.57 0.071 0.69 11.56 0.42 Comp. 188 63.23 2.99 0.86 13.89 0.0096.5 0.07 0.68 11.44 0.42 Comp. 189 63.05 2.9 0.95 13.34 0.01 7.18 0.0760.69 11.4 0.44 Comp. 190 62.69 2.89 0.94 13.79 0.009 7.15 0.076 0.6911.41 0.44

TABLE 25 Table 25: Properties of Adjustable Glass Compositions with CTEin the range of 80-100 × 10⁻⁷/° C. over 20° C. to 300° C. and 20° C. to390° C. Measured Predicted Measured Predicted CTE (20° CTE (20° CTE (20°CTE (20° C.-300° C.) C.-300° C.) C.-390° C.) C.-390° C.) Comp. 172 99.899.51 101.7 101.3 Comp. 173 98.6 98.89 100.8 101.2 Comp. 174 95 94.0097.7 97.3 Comp. 175 90 89.99 92.8 93.0 Comp. 176 85.1 86.79 89.9 89.7Comp. 177 84.5 84.48 86.9 86.8 Comp. 178 83.3 83.87 85.9 86.5 Comp. 17982.7 82.72 85.3 85.4 Comp. 180 82.4 82.14 84.7 84.6 Comp. 181 81.5 81.1284 83.6 Comp. 182 80.3 80.53 82.1 82.3 Comp. 183 80.4 80.03 82.8 82.8Comp. 184 78.9 78.48 80.9 80.4 Comp. 185 82.6 81.79 85 84.3 Comp. 18682.8 83.55 84.9 85.9 Comp. 187 81.9 82.13 84.4 84.7 Comp. 188 83.8 83.8986.6 86.4 Comp. 189 82.8 82.74 85.1 85.2 Comp. 190 84.8 84.54 87 87.1

Standard linear regression analysis was used to construct a predictivemodel for CTE over 20° C. to 300° C. and over 20° C. to 390° C. based onthe compositions provided in Table 24 and corresponding measuredproperties. The regression coefficients that were obtained are providedin Table 26.

TABLE 26 Table 26: Linear Regression Coefficients for CTE over 20° C. to300° C. and 20° C. to 390° C. CTE (20° CTE (20° Oxide C.-300° C.)Coefficient C.-390° C.) Coefficient SiO₂ Intercept 12.4017 Intercept−24.4848 Al₂O₃ X Variable 1 −4.18178 X Variable 1 −0.37352 B₂O₃ XVariable 2 −0.3376 X Variable 2 2.690242 Na₂O X Variable 3 3.983931 XVariable 3 4.298453 K₂O X Variable 4 4.043165 X Variable 4 4.238349 MgOX Variable 5 0.820754 X Variable 5 1.194832 CaO X Variable 6 −64.9976 XVariable 6 −100.006 TiO₂ X Variable 7 49.88685 X Variable 7 69.03159 ZnOX Variable 8 −0.50671 X Variable 8 0.193678

The predicted results from these linear regression models are providedin Table 25 above. As shown in Table 25, each of the glass compositionsis expected to have a CTE between 80×10⁻⁷/° C. and 100×10⁻⁷/° C. Theagreement between the measured and predicted values is shown in FIGS. 14and 15 . Specifically, FIG. 14 is a plot of the measured CTE (Y-axis;values x 10⁻⁷/° C.) as a function of the predicted CTE (X-axis; values x10⁻⁷/° C.) over 20° C. to 300° C. for the glasses from Table 23. FIG. 15is a plot of the measured CTE (Y-axis; values x 10⁻⁷/° C.) as a functionof the predicted CTE (X-axis; values x 10⁻⁷/° C.) over 20° C. to 390° C.for the glasses from Table 23. As may be seen from the R² value for bothof FIGS. 14 and 15 , the model has a high predictive capability for CTEfrom 80-100×10⁻⁷/° C. measured from 20° C. to 300° C. and from 20° C. to390° C.

Example 5

During a production run of the method described above, it was discoveredthat the viscosity of the glass was not conducive to the forming processbeing used. Referring to FIG. 1 , this forming process involved flowingglass from a downcomer 9 into a forming vessel 10 to form a boule. Thesteep viscosity curve of the glass resulted in the boule forms notfilling completely the forming vessel 10. The glass accumulated in thecenter directly beneath the downcomer 9 and would not flow to the edgesof the forming vessel 10. After the forming vessel 10 was allowed tofill for a pre-determined amount of time, the forming vessel 10 wasmoved away from the downcomer 9, and a press was used to force the glassoutward toward the edges of the mold. When the glass viscosity was toohigh, the press was not able to move the glass enough to fill properlythe forming vessel 10, causing boules that did not have the desireddimensions for the boule. An unacceptable boule has a rounded edge and anon-uniform thickness throughout, whereas a properly made boule hasstraight edges and maintains a uniform thickness throughout. To correctthis issue, the steepness of the viscosity curve may be reduced so theglass will flow more during filling of the forming vessel 10 and willremain fluid enough during the subsequent pressing that it will moveoutward to fill the entire forming vessel 10.

Adding fluorine to the glass lowers the viscosity of the glass at bothmelting and forming temperatures; however, the fluorine has a largerimpact at lower temperatures. Thus, fluorine softens the glass more atthe forming temperatures than at melting temperatures, resulting in ashallower viscosity curve. Several glasses at various CTE values weremelted with fluorine (in the form of AlF₃) and properties were measured.Table 27 shows the compositions melted with fluorine along with dataincluding viscosity, coefficient of thermal expansion (CTE) and elasticmodulus. Included in these tables is also the measured CTE and elasticmodulus for the same composition without fluorine. In addition, aliquidus temperature of 1200° C. was measured for Composition 193, theliquid phase of which was a Ca/Na solid solution feldspar.

TABLE 27 Table 27: Compositions with fluorine added and property dataComp. Comp. Comp. Comp. Comp. Comp. Comp. Oxide (wt %) 191 192 193 194195 196 197 SiO₂ 49.56 49.96 47.68 47.65 45.43 45.68 46.39 Al₂O₃ 24.7924.56 24.91 24.86 24.41 24.2 24.61 B₂O₃ 9.75 9.66 9.31 9.24 8.61 8.648.98 Na₂O 3.2 3.8 7.23 7.2 5 4.46 2.69 MgO 3.43 2.83 1.3 1.29 6.53 6.36.43 CaO 8.09 7.99 8.19 8.15 9.38 9.32 9.42 AlF₃ 0.83 0.83 0.75 1.031.29 1.28 1.34 Sb₂O₃ 0.6 0.58 0.51 0.51 0.50 0.5 0.55 Measured CTE w/oF¹ 47.5 49.1 61.6 61.6 58.70 55.9 50.2 (×10⁻⁷/° C.) Measured CTE 47.848.7 62.6 62 60.3 57 51.6 (×10⁻⁷/° C.) Modeled CTE 47.7 49 61.1 60.858.5 56 50.1 (×10⁻⁷/° C.) Measured Young's 80.48 79.10 76 76 85.3 85.786.8 Modulus w/o F¹ (GPa) Measured Young's 79.9 78.3 75.4 75 84.7 84.385.2 Modulus (GPa) Modeled Young's 78.8 77 73.8 73.7 84.6 84 85.6Modulus (GPa) Measured 200 P 1417 N/D² N/D² N/D² N/D² N/D² 1303temperature (° C.) Measured 400 P 1350 N/D² N/D² N/D² N/D² N/D² 1251temperature (° C.) Measured 2000 P 1224 N/D² N/D² N/D² N/D² N/D² 1150temperature (° C.) Measured 4000 P 1179 N/D² N/D² N/D² N/D² N/D² 1113temperature (° C.) Measured 35000 P 1064 N/D² N/D² N/D² N/D² N/D² 1019temperature (° C.) Comp. Comp. Comp. Comp. Comp. Comp. Oxide (wt %) 198199 200 201 202 203 SiO₂ 46.95 44.26 43.98 43.11 42.23 41.77 Al₂O₃ 24.7324.71 24.41 24.34 24.27 24.25 B₂O₃ 8.882 8.82 8.24 7.29 7.18 8.02 Na₂O2.1 4.66 8.69 9.43 10.22 10.23 MgO 6.45 6.46 5.93 5.76 6.07 6 CaO 9.439.39 7.01 8.45 8.33 8.12 AlF₃ 1.28 1.28 1.03 0.97 1.01 1.11 Sb₂O₃ 0.520.51 0.52 0.52 0.52 0.54 Measured CTE w/o F¹ 49.4 57.6 68.6 75 78.4 76.7(×10⁻⁷/° C.) Measured CTE 49 59 71 74.8 78.6 N/D² (×10⁻⁷/° C.) ModeledCTE 48.1 57.5 68.1 72.8 75.8 75.4 (×10⁻⁷/° C.) Measured Young's 87.285.6 80.8 80.5 80.8 80.6 Modulus w/o F¹ (GPa) Measured Young's 86.4 84.980.1 81.7 81.7 N/D² Modulus (GPa) Modeled Young's 86.2 85 80 81 81.180.3 Modulus (GPa) Measured 200 P 1319 1275 1287 1271 1258 N/D²temperature (° C.) Measured 400 P 1265 1223 1227 1212 1200 N/D²temperature (° C.) Measured 2000 P 1162 1121 1113 1100 1088 N/D²temperature (° C.) Measured 4000 P 1126 1084 1073 1061 1049 N/D²temperature (° C.) Measured 35000 P 1031 990 969 961 948 N/D²temperature (° C.) ¹w/o F refers to the same glass composition withoutAlF₃. ²N/D = not determined

FIG. 16 is a plot of the measured CTE of several glasses containingfluorine (Y-axis; values x 10⁻⁷/° C.) versus the CTE of those sameglasses made without fluorine (X-axis; values x 10⁻⁷/° C.). As shown inFIG. 16 , and in particular the trend line slope of about 1.0, theaddition of up to about 1.3 weight % of fluorine does not produce asignificant impact on measured CTE of the glasses. From the size of theerror bars, it is possible to conclude that the difference between theCTE of the glasses with and without fluorine is within the accuracy ofthe measurement system.

FIG. 17 is a plot of the measured elastic modulus of several glassescontaining fluorine (Y-axis; values in GPa) versus the measured elasticmodulus of those same glasses made without fluorine (X-axis; values inGPa). As shown in FIG. 17 , and in particular the trend line slope ofabout 1.0, the addition of up to about 1.3 weight % of fluorine does notproduce a significant impact on measured elastic modulus of the glasses.From the size of the error bars, it is possible to conclude that thedifference between the elastic modulus of the glasses with and withoutfluorine is within the accuracy of the measurement system.

FIG. 18 is a plot of log viscosity (Y-axis; values in Poise) versustemperature (X-axis; values in ° C.) for two of the fluorine-freeproduction glasses, HS5.1 and HS5.9, compared to the same glasscompositions with 1.3 weight % fluorine and a standard production glass,QE. As can be seen in FIG. 18 , the addition of fluorine to the HS5.1and HS5.9 glasses results in a lowering of the glass high temperatureviscosity and also causes a shallowing of the viscosity curve ascompared to the viscosity curve of the glass without fluorine. Thestandard production glass, QE, exhibits the shallowest viscosity curveslope, and thus is the most processable of the tested systems. However,the observed differences in behavior of the glasses with fluorine aresufficient to allow boule production. This change in viscosity was shownto aid forming boules in a production melt.

FIG. 19 is a plot of the predicted CTE (Y-axis; values x 10⁻⁷/° C.)versus the measured CTE (X-axis; values x 10⁻⁷/° C.) for exemplaryfluorine-containing glass compositions. As may be seen from the R² valueof FIG. 19 , the model has a high predictive capability for CTE from50-59×10⁻⁷/° C. measured from 20° C. to 260° C.

FIG. 20 is a plot of the predicted CTE (Y-axis; values x 10⁻⁷/° C.)versus the measured CTE (X-axis; values x 10⁻⁷/° C.) for exemplaryfluorine-containing glass compositions. As may be seen from the R² valueof FIG. 20 , the model has a high predictive capability for CTE from49-62×10⁻⁷/° C. measured from 20° C. to 260° C.

FIG. 21 is a plot of the predicted CTE (Y-axis; values x 10⁻⁷/° C.)versus the measured CTE (X-axis; values x 10⁻⁷/° C.) for exemplaryfluorine-containing glass compositions. As may be seen from the R² valueof FIG. 21 , the model has a high predictive capability for CTE from70-80×10⁻⁷/° C. measured from 20° C. to 260° C.

FIG. 22 is a plot of the predicted CTE (Y-axis; values x 10⁻⁷/° C.)versus the measured CTE (X-axis; values x 10⁻⁷/° C.) for exemplaryfluorine-containing glass compositions. As may be seen from the R² valueof FIG. 22 , the model has a high predictive capability for CTE from68-80×10⁻⁷/° C. measured from 20° C. to 260° C.

FIG. 23 is a plot of the predicted Young's modulus (Y-axis; GPa) versusthe measured Young's modulus (X-axis; GPa) for exemplaryfluorine-containing glass compositions. As may be seen from the R² valueof FIG. 23 , the model has predictive capability for Young's modulus formaterials having a CTE ranging from 50-59×10⁻⁷/° C. measured from 20° C.to 260° C.

FIG. 24 is a plot of the predicted Young's modulus (Y-axis; GPa) versusthe measured Young's modulus (X-axis; GPa) for exemplaryfluorine-containing glass compositions. As may be seen from the R² valueof FIG. 24 , the model has predictive capability for Young's modulus formaterials having a CTE ranging from 49-62×10⁻⁷/° C. measured from 20° C.to 260° C.

FIG. 25 is a plot of the predicted Young's modulus (Y-axis; GPa) versusthe measured Young's modulus (X-axis; GPa) for exemplaryfluorine-containing glass compositions. As may be seen from the R² valueof FIG. 25 , the model has predictive capability for Young's modulus formaterials having a CTE ranging from 70-80×10⁻⁷/° C. measured from 20° C.to 260° C.

FIGS. 26 and 27 are plots of the predicted Young's modulus (Y-axis;GPa), using alternative models, versus the measured Young's modulus(X-axis; GPa) for exemplary fluorine-containing glass compositions. Asmay be seen from the R² value of FIGS. 26 and 27 , these models do nothave significant predictive capability for Young's modulus for materialshaving a CTE ranging from 70-80×10⁻⁷/° C. measured from 20° C. to 260°C. Without intending to be bound by any particular theory, it is believethese correlations were poor due to a limited volume of CTE and Young'smodulus data over this range of glass compositions.

Embodiments described herein include methods for manufacturing glassarticles, having adjustable CTEs and other properties, that may be usedin electronic devices such as semiconductor devices, display devices,sensors, and the like. In some embodiments, the method includes meltinga first glass composition in a melter and feeding a second glasscomposition may into the melter. This second glass composition includesthe same combination of glass constituent components but at least oneglass constituent component has a concentration that is different fromthe concentration of the same component in the first glass composition.Glass articles may be drawn from the melter while maintaining thecontents of the melter in a molten state, including: (1) a first glassarticle that is formed from the first glass composition; (2) at leastone intermediate glass article that is composed of neither the firstglass composition nor the second glass composition and which may bedrawn either simultaneously with the feeding of the second glasscomposition or at some different time; (3) and a final glass articlethat is composed of a composition that is different from the first glasscomposition and may be the same as or different from the second glasscomposition. The concentration of the at least one component in the atleast one intermediate glass article may be between the concentration ofthe at least one component in the first glass composition and theconcentration of the at least one component in the second glasscomposition. The first glass article may have a first set of values fora set of properties. The final glass article may have a second set ofvalues for the same set of properties, the second set of values beingdifferent from the first set of values. The at least one intermediateglass article may have an intermediate set of values for the set ofproperties that is between the first set of values and the second set ofvalues. In the same or different embodiments, the method includesreplacing an amount of a first alkaline earth component or a firstalkali component having a first cation field strength in the molten baseglass composition with an amount of a second alkaline earth component ora second alkali component having a second cation field strength that isdifferent from the first cation field strength, such that glasscompositions with various CTEs can be obtained by making minoradjustments to a base glass composition. Various embodiments may furtheradvantageously provide glass compositions having desirable Young'smodulus and 200 Poise temperatures, which may be predicted based onlinear modeling.

The subject matter recited in the claims is not coextensive with andshould not be interpreted to be coextensive with any embodiment,feature, or combination of features described or illustrated in thisdocument. This is true even if only a single embodiment of the featureor combination of features is illustrated and described in thisdocument.

It will be apparent to those skilled in the art that variousmodifications and variations can be made without departing from thespirit or scope of the claimed subject matter. Accordingly, the claimedsubject matter is not to be restricted except in light of the attachedclaims and their equivalents.

What is claimed is:
 1. A glass article formed from a glass compositioncomprising: greater than or equal to 56 wt. % and less than or equal to66 wt. % SiO₂; greater than or equal to 9.5 wt. % and less than or equalto 12.0 wt. % Al₂O₃; greater than or equal to 3.0 wt. % and less than orequal to 7.5 wt. % Li₂O; greater than or equal to 6 wt. % and less thanor equal to 18 wt. % Na₂O; greater than or equal to 0 wt. % and lessthan or equal to 14 wt. % K₂O; greater than or equal to 0 wt. % and lessthan or equal to 12 wt. % MgO; and greater than or equal to 0 wt. % andless than or equal to 8 wt. % CaO.
 2. The glass article of claim 1,wherein the glass composition comprises greater than or equal to 60 wt.% and less than or equal to 65 wt. % SiO₂
 3. The glass article of claim1, wherein the glass composition comprises greater than or equal to 10wt. % and less than or equal to 12 wt. % Al₂O₃.
 4. The glass article ofclaim 1, wherein the glass composition comprises greater than or equalto 2 wt. % and less than or equal to 4 wt. % B₂O₃.
 5. The glass articleof claim 1, wherein the glass composition comprises greater than orequal to 0 wt. % and less than or equal to 10 wt. % K₂O.
 6. The glassarticle of claim 5, wherein the glass composition comprises greater thanor equal to 0 wt. % and less than or equal to 7 wt. % K₂O.
 7. The glassarticle of claim 1, wherein the glass composition comprises at least onealkaline earth oxide in an amount greater than or equal to 1 wt. % andless than or equal to 22 wt. %.
 8. The glass article of claim 7, whereinthe glass composition comprises at least one alkaline earth oxide in anamount greater than or equal to 9 wt. % and less than or equal to 22 wt.%.
 9. The glass article of claim 1, wherein the glass compositioncomprises greater than or equal to 1 wt. % and less than or equal to 10wt. % MgO.
 10. The glass article of claim 1, wherein the glasscomposition comprises greater than or equal to 0 wt. % and less than orequal to 3 wt. % CaO.
 11. The glass article of claim 1, wherein theglass composition comprises greater than or equal to 3 wt. % and lessthan or equal to 6 wt. % CaO.
 12. The glass article of claim 1, whereinthe glass composition comprises greater than or equal to 0.5 wt. % andless than or equal to 3 wt. % SrO.
 13. The glass article of claim 1,wherein the glass composition comprises greater than or equal to 0.25wt. % and less than or equal to 0.50 wt. % SnO₂.
 14. The glass articleof claim 1, wherein the glass composition comprises less than or equalto 15 wt. % ZnO.
 15. The glass article of claim 14, wherein the glasscomposition comprises less than or equal to 15 wt. % ZrO₂.
 16. The glassarticle of claim 1, wherein the glass composition comprises greater than0 wt. % and less than or equal to 1.5 wt. % AlF₃.
 17. The glass articleof claim 1, wherein the glass article has a Young's modulus of greaterthan or equal to 65 GPa.
 18. The glass article of claim 17, wherein theglass article has a Young's modulus of greater than or equal to 65 GPaand less than or equal to 100 GPa.
 19. The glass article of claim 1wherein the glass article has a 200 Poise temperature of less than 1500°C.
 20. The glass article of claim 1, wherein a CTE of the glass articleis 78 to 100×10⁻⁷/° C. over the range from 20° C. to 260° C.